Abstract

We revisit the problem of intrachannel interactions between solitons in dispersion-managed nonlinear fiber links, which is a major limiting factor for the use of solitons in fiber-optic networks. By means of systematic simulations, we demonstrate the existence of a well-defined maximum of the interaction length, zint, as a function of the ratio of peak powers of interacting solitons, while in the case of identical solitons the interaction length always attains a minimum. An explanation to these features is proposed. Interaction effects in three-soliton sets are studied too. The results suggest that the transmission characteristics of soliton streams in the dispersion-managed system may be improved by using alternating values of the peak powers whose ratio corresponds to the maximum of zint.

© 2010 Optical Society of America

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2008

R. Ganapathy, K. Porsezian, A. Hasegawa, and V. N. Serkin, “Soliton interaction under soliton dispersion management,” IEEE J. Quantum Electron. 44, 383-390 (2008).
[CrossRef]

2006

2005

2004

2003

2002

2001

2000

T. I. Lakoba and G. P. Agrawal, “Optimization of the average-dispersion range for long-haul dispersion-managed soliton systems,” J. Lightwave Technol. 18, 1504-1512 (2000).
[CrossRef]

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, “Tuning of in-line filter position for dispersion-managed soliton transmission,” Opt. Commun. 175, 103-108 (2000).
[CrossRef]

T. Hirooka and S. Wabnitz, “Nonlinear gain control of dispersion-managed soliton amplitude and collisions,” Opt. Fiber Technol. 6, 109-121 (2000).
[CrossRef]

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photonics Technol. Lett. 12, 299-301 (2000).
[CrossRef]

S. Wabnitz and F. Neddam, “Pulse interactions and collisions in asymmetric higher-order dispersion managed fiber link,” Opt. Commun. 183, 395-405 (2000).
[CrossRef]

H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330-336 (2000).
[CrossRef]

E. M. Gromov and V. I. Talanov, “Short optical solitons in fibers,” Chaos 10, 551-558 (2000).
[CrossRef]

1999

1998

T. Georges, “Soliton interaction in dispersion-managed links,” J. Opt. Soc. Am. B 15, 1553-1560 (1998).
[CrossRef]

M. Matsumoto, “Analysis of interaction between stretched pulses propagating in dispersion-managed fibers,” IEEE Photonics Technol. Lett. 10, 373-375 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481-482 (1998).
[CrossRef]

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of soliton transmissions in dispersion-managed fiber links,” Opt. Commun. 145, 48-52 (1998).
[CrossRef]

B. A. Malomed, “Suppression of soliton jitter and interactions by means of dispersion management,” Opt. Commun. 147, 157-162 (1998).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366-375 (1998).
[CrossRef]

T. Okamawari, A. Maruta, and Y. Kodama, “Analysis of Gordon-Haus jitter in a dispersion-compensated optical transmission system,” Opt. Lett. 23, 694-696 (1998).
[CrossRef]

T. Hirooka and A. Hasegawa, “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems,” Opt. Lett. 23, 768-770 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900-902 (1998).
[CrossRef]

S. Kumar, M. Wald, F. Lederer, and A. Hasegawa, “Soliton interaction in strongly dispersion-managed optical fibers,” Opt. Lett. 23, 1019-1021 (1998).
[CrossRef]

B. A. Malomed, “Jitter suppression by guiding filters in combination with dispersion management,” Opt. Lett. 23, 1250-1252 (1998).
[CrossRef]

A. M. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, and N. J. Doran, “Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,” Opt. Lett. 23, 1354-1356 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

1997

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793-795 (1997).
[CrossRef] [PubMed]

S. Kumar and F. Lederer, “Gordon-Haus effect in dispersion-managed soliton systems,” Opt. Lett. 22, 1870-1872 (1997).
[CrossRef]

A. Mostofi and P. L. Chu, “Reversal of soliton interactions in optically phase-conjugated systems with unequal-amplitude and alternating-phase solitons,” Opt. Commun. 141, 259-264 (1997).
[CrossRef]

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735-737 (1997).
[CrossRef]

1996

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54-55 (1996).
[CrossRef]

V. S. Dimitrov, D. Y. Dakova, and I. M. Uzunov, “On the description of interaction in sequences of unequal soliton-like pulses,” Opt. Quantum Electron. 28, 1765-1771 (1996).
[CrossRef]

1995

A. D. Boardman, H. M. Mehta, A. K. Sangarpaul, R. Putman, and K. Xie, “Interactions in bright N-soliton trains propagating in birefringent optical fibers,” Opt. Commun. 116, 208-218 (1995).
[CrossRef]

A. Berntson, D. Anderson, and M. Lisak, “Analysis of coherent and incoherent interactions of amplitude shifted solitons in optical fibers,” Phys. Scr. 52, 544-553 (1995).
[CrossRef]

1994

1993

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “Influence of the initial phase difference between pulses in the N-soliton interaction in trains of unequal solitons in optical fibers,” Opt. Commun. 97, 307-311 (1993).
[CrossRef]

1992

1985

P. L. Chu and C. Desem, “Mutual interaction between solitons of unequal amplitudes in optical fiber,” Electron. Lett. 21, 1133-1134 (1985).
[CrossRef]

Ablowitz, M. J.

Adali, T.

Afanasjev, V. V.

Agrawal, G. P.

Anderson, D.

A. Berntson, D. Anderson, and M. Lisak, “Analysis of coherent and incoherent interactions of amplitude shifted solitons in optical fibers,” Phys. Scr. 52, 544-553 (1995).
[CrossRef]

Atai, J.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E 65, 036605 (2002).
[CrossRef]

Bayvel, P.

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54-55 (1996).
[CrossRef]

Berntson, A.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481-482 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900-902 (1998).
[CrossRef]

A. Berntson, D. Anderson, and M. Lisak, “Analysis of coherent and incoherent interactions of amplitude shifted solitons in optical fibers,” Phys. Scr. 52, 544-553 (1995).
[CrossRef]

Biondini, G.

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54-55 (1996).
[CrossRef]

Boardman, A. D.

A. D. Boardman, H. M. Mehta, A. K. Sangarpaul, R. Putman, and K. Xie, “Interactions in bright N-soliton trains propagating in birefringent optical fibers,” Opt. Commun. 116, 208-218 (1995).
[CrossRef]

Cai, Y.

Capobianco, A. D.

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, “Tuning of in-line filter position for dispersion-managed soliton transmission,” Opt. Commun. 175, 103-108 (2000).
[CrossRef]

Carter, G. M.

Chen, P. Y. P.

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, “An iterative numerical method for dispersion managed solitons,” Opt. Commun. 245, 425-435 (2005).
[CrossRef]

Chen, Y.

Chu, P. L.

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, “An iterative numerical method for dispersion managed solitons,” Opt. Commun. 245, 425-435 (2005).
[CrossRef]

A. Mostofi and P. L. Chu, “Reversal of soliton interactions in optically phase-conjugated systems with unequal-amplitude and alternating-phase solitons,” Opt. Commun. 141, 259-264 (1997).
[CrossRef]

P. L. Chu and C. Desem, “Mutual interaction between solitons of unequal amplitudes in optical fiber,” Electron. Lett. 21, 1133-1134 (1985).
[CrossRef]

Dakova, D. Y.

V. S. Dimitrov, D. Y. Dakova, and I. M. Uzunov, “On the description of interaction in sequences of unequal soliton-like pulses,” Opt. Quantum Electron. 28, 1765-1771 (1996).
[CrossRef]

Del Duce, A.

Desem, C.

P. L. Chu and C. Desem, “Mutual interaction between solitons of unequal amplitudes in optical fiber,” Electron. Lett. 21, 1133-1134 (1985).
[CrossRef]

Dimitrov, V. S.

V. S. Dimitrov, D. Y. Dakova, and I. M. Uzunov, “On the description of interaction in sequences of unequal soliton-like pulses,” Opt. Quantum Electron. 28, 1765-1771 (1996).
[CrossRef]

Docherty, A.

Doran, N. J.

H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330-336 (2000).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900-902 (1998).
[CrossRef]

A. M. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, and N. J. Doran, “Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,” Opt. Lett. 23, 1354-1356 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481-482 (1998).
[CrossRef]

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54-55 (1996).
[CrossRef]

Edagawa, N.

Efremidis, N.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E 65, 036605 (2002).
[CrossRef]

Ereifej, H. N.

Fedoruk, M. P.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” Comptes Rendue Physique 4, 145-161 (2003).
[CrossRef]

Forysiak, W.

H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330-336 (2000).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900-902 (1998).
[CrossRef]

A. M. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, and N. J. Doran, “Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,” Opt. Lett. 23, 1354-1356 (1998).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481-482 (1998).
[CrossRef]

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

Frantzeskakis, D. J.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E 65, 036605 (2002).
[CrossRef]

Fujii, K.

H. Murai, H. T. Yamada, and K. Fujii, “Analysis and experiment on soliton-based WDM transmission employing initial phase alternation with OTDM techniques,” IEICE Trans. Communications E 85B, 438-445 (2002).

Ganapathy, R.

R. Ganapathy, K. Porsezian, A. Hasegawa, and V. N. Serkin, “Soliton interaction under soliton dispersion management,” IEEE J. Quantum Electron. 44, 383-390 (2008).
[CrossRef]

Georges, T.

Gloag, A. J.

Golovchenko, E. A.

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793-795 (1997).
[CrossRef] [PubMed]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735-737 (1997).
[CrossRef]

Grigoryan, V. S.

Gromov, E. M.

E. M. Gromov and V. I. Talanov, “Short optical solitons in fibers,” Chaos 10, 551-558 (2000).
[CrossRef]

Hasegawa, A.

Haus, H. A.

Hirooka, T.

T. Hirooka and S. Wabnitz, “Nonlinear gain control of dispersion-managed soliton amplitude and collisions,” Opt. Fiber Technol. 6, 109-121 (2000).
[CrossRef]

T. Hirooka and A. Hasegawa, “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems,” Opt. Lett. 23, 768-770 (1998).
[CrossRef]

Hizanidis, K.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E 65, 036605 (2002).
[CrossRef]

Holzlohner, R.

Inoue, T.

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photonics Technol. Lett. 12, 299-301 (2000).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547-1559 (1999).
[CrossRef]

Kato, H.

Kaup, D. J.

D. J. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366-375 (1998).
[CrossRef]

Killey, R. I.

Knox, F. M.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54-55 (1996).
[CrossRef]

Kodama, Y.

Kschischang, F. R.

Kumar, S.

Lakoba, T.

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366-375 (1998).
[CrossRef]

Lakoba, T. I.

Lederer, F.

Lisak, M.

A. Berntson, D. Anderson, and M. Lisak, “Analysis of coherent and incoherent interactions of amplitude shifted solitons in optical fibers,” Phys. Scr. 52, 544-553 (1995).
[CrossRef]

Liu, X.

Malomed, B.

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31-36 (1999).
[CrossRef]

Malomed, B. A.

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, “An iterative numerical method for dispersion managed solitons,” Opt. Commun. 245, 425-435 (2005).
[CrossRef]

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E 65, 036605 (2002).
[CrossRef]

M. Wald, B. A. Malomed, and F. Lederer, “Interaction of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,” Opt. Lett. 26, 965-967 (2001).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

B. A. Malomed, “Jitter suppression by guiding filters in combination with dispersion management,” Opt. Lett. 23, 1250-1252 (1998).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366-375 (1998).
[CrossRef]

B. A. Malomed, “Suppression of soliton jitter and interactions by means of dispersion management,” Opt. Commun. 147, 157-162 (1998).
[CrossRef]

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

Mamyshev, P. V.

Mamysheva, N. A.

Maruta, A.

Matera, F.

Matsumoto, M.

M. Matsumoto, “Analysis of interaction between stretched pulses propagating in dispersion-managed fibers,” IEEE Photonics Technol. Lett. 10, 373-375 (1998).
[CrossRef]

McKinstrie, C. J.

Medvedev, S. B.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” Comptes Rendue Physique 4, 145-161 (2003).
[CrossRef]

Mehta, H. M.

A. D. Boardman, H. M. Mehta, A. K. Sangarpaul, R. Putman, and K. Xie, “Interactions in bright N-soliton trains propagating in birefringent optical fibers,” Opt. Commun. 116, 208-218 (1995).
[CrossRef]

Menyuk, C. R.

O. V. Sinkin, V. S. Grigoryan, J. Zweck, C. R. Menyuk, A. Docherty, and M. J. Ablowitz, “Calculation, characterization, and application of the time shift function in wavelength-division-multiplexed return-to-zero systems,” Opt. Lett. 30, 2056-2058 (2005).
[CrossRef] [PubMed]

O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21, 61-68 (2003).
[CrossRef]

R. Holzlohner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and theoretical characterization of a 40-Gb/s long-haul single-channel transmission system,” J. Lightwave Technol. 20, 1124-1131 (2002).
[CrossRef]

R. M. Mu and C. R. Menyuk, “Convergence of the chirped return-to-zero and dispersion managed soliton modulation formats in WDM systems,” J. Lightwave Technol. 20, 608-617 (2002).
[CrossRef]

Y. Cai, T. Adali, C. R. Menyuk, and J. M. Morris, “Sliding window criterion codes and concatenation scheme for mitigating timing-jitter-induced errors in WDM fiber transmissions,” J. Lightwave Technol. 20, 201-212 (2002).
[CrossRef]

O. V. Sinkin, J. Zweck, and C. R. Menyuk, “Comparative study of pulse interactions in optical fiber transmission systems with different modulation formats,” Opt. Express 9, 339-352 (2001).
[CrossRef] [PubMed]

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793-795 (1997).
[CrossRef] [PubMed]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735-737 (1997).
[CrossRef]

Mezentsev, V. K.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” Comptes Rendue Physique 4, 145-161 (2003).
[CrossRef]

Mollenauer, L. F.

Morita, I.

Morris, J. M.

Mostofi, A.

A. Mostofi and P. L. Chu, “Reversal of soliton interactions in optically phase-conjugated systems with unequal-amplitude and alternating-phase solitons,” Opt. Commun. 141, 259-264 (1997).
[CrossRef]

Mu, R. M.

Murai, H.

H. Murai, H. T. Yamada, and K. Fujii, “Analysis and experiment on soliton-based WDM transmission employing initial phase alternation with OTDM techniques,” IEICE Trans. Communications E 85B, 438-445 (2002).

Neddam, F.

S. Wabnitz and F. Neddam, “Pulse interactions and collisions in asymmetric higher-order dispersion managed fiber link,” Opt. Commun. 183, 395-405 (2000).
[CrossRef]

Niculae, A. M.

Nijhof, H. B.

H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330-336 (2000).
[CrossRef]

Nijhof, J. H. B.

Nistazakis, H. E.

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E 65, 036605 (2002).
[CrossRef]

Okamawari, T.

Olson, E. S.

Orenstein, M.

Pechenkin, V.

Pilipetskii, A. N.

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793-795 (1997).
[CrossRef] [PubMed]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735-737 (1997).
[CrossRef]

Porsezian, K.

R. Ganapathy, K. Porsezian, A. Hasegawa, and V. N. Serkin, “Soliton interaction under soliton dispersion management,” IEEE J. Quantum Electron. 44, 383-390 (2008).
[CrossRef]

Putman, R.

A. D. Boardman, H. M. Mehta, A. K. Sangarpaul, R. Putman, and K. Xie, “Interactions in bright N-soliton trains propagating in birefringent optical fibers,” Opt. Commun. 116, 208-218 (1995).
[CrossRef]

Sangarpaul, A. K.

A. D. Boardman, H. M. Mehta, A. K. Sangarpaul, R. Putman, and K. Xie, “Interactions in bright N-soliton trains propagating in birefringent optical fibers,” Opt. Commun. 116, 208-218 (1995).
[CrossRef]

Scheuer, J.

Serkin, V. N.

R. Ganapathy, K. Porsezian, A. Hasegawa, and V. N. Serkin, “Soliton interaction under soliton dispersion management,” IEEE J. Quantum Electron. 44, 383-390 (2008).
[CrossRef]

Settembre, M.

Shapiro, E. G.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” Comptes Rendue Physique 4, 145-161 (2003).
[CrossRef]

Sinkin, O. V.

Smith, N. J.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54-55 (1996).
[CrossRef]

Stoev, V. D.

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “Influence of the initial phase difference between pulses in the N-soliton interaction in trains of unequal solitons in optical fibers,” Opt. Commun. 97, 307-311 (1993).
[CrossRef]

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “N-soliton interaction in trains of unequal pulses in optical fibers,” Opt. Lett. 17, 1417-1419 (1992).
[CrossRef] [PubMed]

Sugahara, H.

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photonics Technol. Lett. 12, 299-301 (2000).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547-1559 (1999).
[CrossRef]

Suzuki, M.

Talanov, V. I.

E. M. Gromov and V. I. Talanov, “Short optical solitons in fibers,” Chaos 10, 551-558 (2000).
[CrossRef]

Tanaka, K.

Tonello, A.

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, “Tuning of in-line filter position for dispersion-managed soliton transmission,” Opt. Commun. 175, 103-108 (2000).
[CrossRef]

Turitsyn, S. K.

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” Comptes Rendue Physique 4, 145-161 (2003).
[CrossRef]

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, “Tuning of in-line filter position for dispersion-managed soliton transmission,” Opt. Commun. 175, 103-108 (2000).
[CrossRef]

Tzoleva, T. I.

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “Influence of the initial phase difference between pulses in the N-soliton interaction in trains of unequal solitons in optical fibers,” Opt. Commun. 97, 307-311 (1993).
[CrossRef]

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “N-soliton interaction in trains of unequal pulses in optical fibers,” Opt. Lett. 17, 1417-1419 (1992).
[CrossRef] [PubMed]

Uzunov, I. M.

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of soliton transmissions in dispersion-managed fiber links,” Opt. Commun. 145, 48-52 (1998).
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V. S. Dimitrov, D. Y. Dakova, and I. M. Uzunov, “On the description of interaction in sequences of unequal soliton-like pulses,” Opt. Quantum Electron. 28, 1765-1771 (1996).
[CrossRef]

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “Influence of the initial phase difference between pulses in the N-soliton interaction in trains of unequal solitons in optical fibers,” Opt. Commun. 97, 307-311 (1993).
[CrossRef]

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “N-soliton interaction in trains of unequal pulses in optical fibers,” Opt. Lett. 17, 1417-1419 (1992).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wabnitz, S.

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, “Tuning of in-line filter position for dispersion-managed soliton transmission,” Opt. Commun. 175, 103-108 (2000).
[CrossRef]

T. Hirooka and S. Wabnitz, “Nonlinear gain control of dispersion-managed soliton amplitude and collisions,” Opt. Fiber Technol. 6, 109-121 (2000).
[CrossRef]

S. Wabnitz and F. Neddam, “Pulse interactions and collisions in asymmetric higher-order dispersion managed fiber link,” Opt. Commun. 183, 395-405 (2000).
[CrossRef]

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of soliton transmissions in dispersion-managed fiber links,” Opt. Commun. 145, 48-52 (1998).
[CrossRef]

Wald, M.

M. Wald, B. A. Malomed, and F. Lederer, “Interaction of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,” Opt. Lett. 26, 965-967 (2001).
[CrossRef]

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31-36 (1999).
[CrossRef]

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of soliton transmissions in dispersion-managed fiber links,” Opt. Commun. 145, 48-52 (1998).
[CrossRef]

S. Kumar, M. Wald, F. Lederer, and A. Hasegawa, “Soliton interaction in strongly dispersion-managed optical fibers,” Opt. Lett. 23, 1019-1021 (1998).
[CrossRef]

Wei, X.

Xie, C. J.

Xie, K.

A. D. Boardman, H. M. Mehta, A. K. Sangarpaul, R. Putman, and K. Xie, “Interactions in bright N-soliton trains propagating in birefringent optical fibers,” Opt. Commun. 116, 208-218 (1995).
[CrossRef]

Yamada, H. T.

H. Murai, H. T. Yamada, and K. Fujii, “Analysis and experiment on soliton-based WDM transmission employing initial phase alternation with OTDM techniques,” IEICE Trans. Communications E 85B, 438-445 (2002).

Yang, J.

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366-375 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

Yu, T.

Zitelli, M.

Zweck, J.

Chaos

E. M. Gromov and V. I. Talanov, “Short optical solitons in fibers,” Chaos 10, 551-558 (2000).
[CrossRef]

Comptes Rendue Physique

S. K. Turitsyn, E. G. Shapiro, S. B. Medvedev, M. P. Fedoruk, and V. K. Mezentsev, “Physics and mathematics of dispersion-managed optical solitons,” Comptes Rendue Physique 4, 145-161 (2003).
[CrossRef]

Electron. Lett.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, “Enhanced power solitons in optical fibres with periodic dispersion management,” Electron. Lett. 32, 54-55 (1996).
[CrossRef]

E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission,” Electron. Lett. 33, 735-737 (1997).
[CrossRef]

P. L. Chu and C. Desem, “Mutual interaction between solitons of unequal amplitudes in optical fiber,” Electron. Lett. 21, 1133-1134 (1985).
[CrossRef]

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, “Energy enhancement of dispersion-managed solitons and WDM,” Electron. Lett. 34, 481-482 (1998).
[CrossRef]

IEEE J. Quantum Electron.

R. Ganapathy, K. Porsezian, A. Hasegawa, and V. N. Serkin, “Soliton interaction under soliton dispersion management,” IEEE J. Quantum Electron. 44, 383-390 (2008).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. B. Nijhof, W. Forysiak, and N. J. Doran, “The averaging method for finding exactly periodic dispersion-managed solitons,” IEEE J. Sel. Top. Quantum Electron. 6, 330-336 (2000).
[CrossRef]

IEEE Photonics Technol. Lett.

M. Matsumoto, “Analysis of interaction between stretched pulses propagating in dispersion-managed fibers,” IEEE Photonics Technol. Lett. 10, 373-375 (1998).
[CrossRef]

T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama, “Interactions between dispersion managed solitons in optical-time-division-multiplexed system,” IEEE Photonics Technol. Lett. 12, 299-301 (2000).
[CrossRef]

IEICE Trans. Communications E

H. Murai, H. T. Yamada, and K. Fujii, “Analysis and experiment on soliton-based WDM transmission employing initial phase alternation with OTDM techniques,” IEICE Trans. Communications E 85B, 438-445 (2002).

J. Lightwave Technol.

N. J. Smith, N. J. Doran, W. Forysiak, and F. M. Knox, “Soliton transmission using periodic dispersion compensation,” J. Lightwave Technol. 15, 1808-1822 (1997).
[CrossRef]

T. I. Lakoba and G. P. Agrawal, “Optimization of the average-dispersion range for long-haul dispersion-managed soliton systems,” J. Lightwave Technol. 18, 1504-1512 (2000).
[CrossRef]

H. Sugahara, H. Kato, T. Inoue, A. Maruta, and Y. Kodama, “Optimal dispersion management for a wavelength division multiplexed optical soliton transmission system,” J. Lightwave Technol. 17, 1547-1559 (1999).
[CrossRef]

M. Zitelli, F. Matera, and M. Settembre, “Single-channel transmission in dispersion management links in conditions of very strong pulse broadening: application to 40 Gb/s signals on step-index fibers,” J. Lightwave Technol. 17, 2498-2505 (1999).
[CrossRef]

I. Morita, K. Tanaka, N. Edagawa, and M. Suzuki, “40 Gb/s single-channel soliton transmission over transoceanic distances by reducing Gordon-Haus timing jitter and soliton-soliton interaction,” J. Lightwave Technol. 17, 2506-2511 (1999).
[CrossRef]

Y. Cai, T. Adali, C. R. Menyuk, and J. M. Morris, “Sliding window criterion codes and concatenation scheme for mitigating timing-jitter-induced errors in WDM fiber transmissions,” J. Lightwave Technol. 20, 201-212 (2002).
[CrossRef]

R. M. Mu and C. R. Menyuk, “Convergence of the chirped return-to-zero and dispersion managed soliton modulation formats in WDM systems,” J. Lightwave Technol. 20, 608-617 (2002).
[CrossRef]

R. Holzlohner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and theoretical characterization of a 40-Gb/s long-haul single-channel transmission system,” J. Lightwave Technol. 20, 1124-1131 (2002).
[CrossRef]

O. V. Sinkin, R. Holzlohner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21, 61-68 (2003).
[CrossRef]

A. Del Duce, R. I. Killey, and P. Bayvel, “Comparison of nonlinear pulse interactions in 160-Gb/s quasi-linear and dispersion managed soliton systems,” J. Lightwave Technol. 22, 1263-1271 (2004).
[CrossRef]

V. Pechenkin and F. R. Kschischang, “Higher bit rates for dispersion-managed soliton communication systems via constrained coding,” J. Lightwave Technol. 24, 1149-1158 (2006).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

M. Wald, B. Malomed, and F. Lederer, “Interaction of moderately dispersion managed solitons,” Opt. Commun. 172, 31-36 (1999).
[CrossRef]

S. Wabnitz and F. Neddam, “Pulse interactions and collisions in asymmetric higher-order dispersion managed fiber link,” Opt. Commun. 183, 395-405 (2000).
[CrossRef]

M. Wald, I. M. Uzunov, F. Lederer, and S. Wabnitz, “Optimization of soliton transmissions in dispersion-managed fiber links,” Opt. Commun. 145, 48-52 (1998).
[CrossRef]

B. A. Malomed, “Suppression of soliton jitter and interactions by means of dispersion management,” Opt. Commun. 147, 157-162 (1998).
[CrossRef]

A. Tonello, A. D. Capobianco, S. Wabnitz, and S. K. Turitsyn, “Tuning of in-line filter position for dispersion-managed soliton transmission,” Opt. Commun. 175, 103-108 (2000).
[CrossRef]

P. Y. P. Chen, P. L. Chu, and B. A. Malomed, “An iterative numerical method for dispersion managed solitons,” Opt. Commun. 245, 425-435 (2005).
[CrossRef]

T. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary pulse propagation in the strong dispersion management regime,” Opt. Commun. 149, 366-375 (1998).
[CrossRef]

A. Mostofi and P. L. Chu, “Reversal of soliton interactions in optically phase-conjugated systems with unequal-amplitude and alternating-phase solitons,” Opt. Commun. 141, 259-264 (1997).
[CrossRef]

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “Influence of the initial phase difference between pulses in the N-soliton interaction in trains of unequal solitons in optical fibers,” Opt. Commun. 97, 307-311 (1993).
[CrossRef]

A. D. Boardman, H. M. Mehta, A. K. Sangarpaul, R. Putman, and K. Xie, “Interactions in bright N-soliton trains propagating in birefringent optical fibers,” Opt. Commun. 116, 208-218 (1995).
[CrossRef]

Opt. Express

Opt. Fiber Technol.

T. Hirooka and S. Wabnitz, “Nonlinear gain control of dispersion-managed soliton amplitude and collisions,” Opt. Fiber Technol. 6, 109-121 (2000).
[CrossRef]

Opt. Lett.

I. M. Uzunov, V. D. Stoev, and T. I. Tzoleva, “N-soliton interaction in trains of unequal pulses in optical fibers,” Opt. Lett. 17, 1417-1419 (1992).
[CrossRef] [PubMed]

T. Yu, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk, “Dispersion-managed soliton interactions in optical fibers,” Opt. Lett. 22, 793-795 (1997).
[CrossRef] [PubMed]

S. Kumar and F. Lederer, “Gordon-Haus effect in dispersion-managed soliton systems,” Opt. Lett. 22, 1870-1872 (1997).
[CrossRef]

T. Okamawari, A. Maruta, and Y. Kodama, “Analysis of Gordon-Haus jitter in a dispersion-compensated optical transmission system,” Opt. Lett. 23, 694-696 (1998).
[CrossRef]

T. Hirooka and A. Hasegawa, “Chirped soliton interaction in strongly dispersion-managed wavelength-division-multiplexing systems,” Opt. Lett. 23, 768-770 (1998).
[CrossRef]

A. Berntson, N. J. Doran, W. Forysiak, and J. H. B. Nijhof, “Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion,” Opt. Lett. 23, 900-902 (1998).
[CrossRef]

S. Kumar, M. Wald, F. Lederer, and A. Hasegawa, “Soliton interaction in strongly dispersion-managed optical fibers,” Opt. Lett. 23, 1019-1021 (1998).
[CrossRef]

B. A. Malomed, “Jitter suppression by guiding filters in combination with dispersion management,” Opt. Lett. 23, 1250-1252 (1998).
[CrossRef]

A. M. Niculae, W. Forysiak, A. J. Gloag, J. H. B. Nijhof, and N. J. Doran, “Soliton collisions with wavelength-division multiplexed systems with strong dispersion management,” Opt. Lett. 23, 1354-1356 (1998).
[CrossRef]

D. J. Kaup, B. A. Malomed, and J. Yang, “Interchannel pulse collision in a wavelength-division-multiplexed system with strong dispersion management,” Opt. Lett. 23, 1600-1602 (1998).
[CrossRef]

Y. Chen and H. A. Haus, “Collisions in dispersion-managed soliton propagation,” Opt. Lett. 24, 217-219 (1999).
[CrossRef]

P. V. Mamyshev and L. F. Mollenauer, “Soliton collisions in wavelength-division-multiplexed dispersion-managed systems,” Opt. Lett. 24, 448-450 (1999).
[CrossRef]

P. V. Mamyshev and N. A. Mamysheva, “Pulse-overlapped dispersion-managed data transmission and intrachannel four-wave mixing,” Opt. Lett. 24, 1454-1456 (1999).
[CrossRef]

O. V. Sinkin, V. S. Grigoryan, J. Zweck, C. R. Menyuk, A. Docherty, and M. J. Ablowitz, “Calculation, characterization, and application of the time shift function in wavelength-division-multiplexed return-to-zero systems,” Opt. Lett. 30, 2056-2058 (2005).
[CrossRef] [PubMed]

M. Wald, B. A. Malomed, and F. Lederer, “Interaction of dispersion-managed solitons in wavelength-division-multiplexed optical transmission lines,” Opt. Lett. 26, 965-967 (2001).
[CrossRef]

X. Liu, X. Wei, L. F. Mollenauer, C. J. McKinstrie, and C. J. Xie, “Collision-induced time shift of a dispersion-managed soliton and its minimization in wavelength-division-multiplexed transmission,” Opt. Lett. 28, 1412-1414 (2003).
[CrossRef] [PubMed]

Opt. Quantum Electron.

V. S. Dimitrov, D. Y. Dakova, and I. M. Uzunov, “On the description of interaction in sequences of unequal soliton-like pulses,” Opt. Quantum Electron. 28, 1765-1771 (1996).
[CrossRef]

Phys. Rev. E

H. E. Nistazakis, D. J. Frantzeskakis, J. Atai, B. A. Malomed, N. Efremidis, and K. Hizanidis, “Multichannel pulse dynamics in a stabilized Ginzburg-Landau system,” Phys. Rev. E 65, 036605 (2002).
[CrossRef]

Phys. Scr.

A. Berntson, D. Anderson, and M. Lisak, “Analysis of coherent and incoherent interactions of amplitude shifted solitons in optical fibers,” Phys. Scr. 52, 544-553 (1995).
[CrossRef]

Other

B. A. Malomed, Soliton Management in Periodic Systems (Springer, 2006).

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Figures (9)

Fig. 1
Fig. 1

The standard periodic dispersion-management (DM) scheme. The distribution of the local GVD coefficient is shown, and the DM cell is defined.

Fig. 2
Fig. 2

The evolution of a stable DM soliton is shown over two DM cells. It was created by launching Gaussian pulse (4), with A 0 = 1.16 and a 0 = 3.41 , into the system with PAD β ¯ = 0.1 . In the established state, this soliton has peak power P = 1.30 , minimum width T FWHM = 1.32 , and DM strength S = 1.14 . The same soliton appears as a narrower one in the example of the interaction displayed in Fig. 3.

Fig. 3
Fig. 3

An example of the intrachannel interaction between two solitons, with initial separation Δ T 0 = 5 , ending by the collision. Here and below, the transmission distance is shown in units of the DM period. The two solitons are generated by inputs (4) with ( A 0 ) 1 = 0.78 , ( a 0 ) 1 = 2.25 and ( A 0 ) 2 = 1.16 , ( a 0 ) 2 = 3.41 . Peak powers, widths, and DM strengths of the respective stable DM solitons are, severally, P 1 = 0.61 , ( T FWHM ) 1 = 1.58 , S 1 = 0.80 , and P 2 = 1.30 , ( T FWHM ) 2 = 1.32 , S 2 = 1.14 (the latter soliton is the same one as in Fig. 2). PAD is β ¯ = 0.1 .

Fig. 4
Fig. 4

The dependence of the interaction distance, Z z int , as defined in the text, on the ratio of the peak powers of two solitons, in the system with PAD β ¯ = 0.1 . Minimum and maximum points are marked by arrows. The inset in panel (a) is a zoom of the plot around the deep minimum. The initial temporal separation between the solitons is (a) Δ T 0 = 5 and (b) Δ T 0 = 6 . In both panels, P 2 varies, while parameters of the first soliton (for the definiteness’ sake, it is chosen as the one in the delayed position, in the temporal domain, cf. Fig. 3), are fixed: P 1 = 0.68 , ( T FWHM ) 1 = 1.53 , S 1 = 0.85 in (a), and P 1 = 0.65 , ( T FWHM ) 1 = 1.55 , S 1 = 0.83 in (b). Recall S is the DM strength defined as per Eq. (5).

Fig. 5
Fig. 5

The same as in Fig. 4a, but for different values of PAD: (a) β ¯ = 0.2 and (b) β ¯ = 0.05 . The fixed parameters of the first soliton are P 1 = 1.51 , ( T FWHM ) 1 = 1.44 , S 1 = 0.96 in (a), and P 1 = 0.35 , ( T FWHM ) 1 = 1.56 , S 1 = 0.83 in (b).

Fig. 6
Fig. 6

The interaction length versus power P 2 for fixed parameters of the other soliton and initial separation between the solitons Δ T 0 = 5 . In (a), β ¯ = 0.2 , and the thin continuous curve corresponds to P 1 = 1.23 , ( T FWHM ) 1 = 1.53 , S 1 = 0.86 ; the thin dashed curve corresponds to P 1 = 1.45 , ( T FWHM ) 1 = 1.46 , S 1 = 0.94 ; the dotted curve corresponds to P 1 = 1.59 , ( T FWHM ) 1 = 1.42 , S 1 = 0.99 [this curve is close to the one in Fig. 5a]; and the bold continuous curve corresponds to P 1 = 2.23 , ( T FWHM ) 1 = 1.30 , S 1 = 1.18 . In (b), β ¯ = 0.1 , with the thin continuous curve corresponding to P 1 = 0.50 , ( T FWHM ) 1 = 1.66 , S 1 = 0.73 ; the thin dashed curve corresponding to P 1 = 0.59 , ( T FWHM ) 1 = 1.59 , S 1 = 0.79 ; the dotted curve corresponding to P 1 = 0.68 , ( T FWHM ) 1 = 1.53 , S 1 = 0.85 [this curve is actually tantamount to the one in Fig. 4a]; the bold continuous curve corresponding to P 1 = 0.81 , ( T FWHM ) 1 = 1.47 , S 1 = 0.93 ; and the bold dashed curve corresponding to P 1 = 0.98 , ( T FWHM ) 1 = 1.41 , S 1 = 1.01 . In (c), β ¯ = 0.05 , with the thin continuous curve corresponding to P 1 = 0.28 , ( T FWHM ) 1 = 1.63 , S 1 = 0.75 ; the thin dashed curve—to P 1 = 0.30 , ( T FWHM ) 1 = 1.61 , S 1 = 0.77 ; the dotted curve—to P 1 = 0.32 , ( T FWHM ) 1 = 1.58 , S 1 = 0.79 ; the bold continuous curve—to P 1 = 0.35 , ( T FWHM ) 1 = 1.56 , S 1 = 0.82 [this curve is very close to one shown in Fig. 5b]; the bold dashed curve—to P 1 = 0.38 , ( T FWHM ) 1 = 1.53 , S 1 = 0.86 ; and the curve composed of short rods (it looks like the lower dotted curve) corresponds to P 1 = 0.42 , ( T FWHM ) 1 = 1.49 , S 1 = 0.90 .

Fig. 7
Fig. 7

The interaction length versus power P for pairs of identical solitons, in the system with β ¯ = 0.2 (a), β ¯ = 0.1 (b), and β ¯ = 0.05 (c). In all the cases, the initial separation between the solitons is Δ T 0 = 5 .

Fig. 8
Fig. 8

The same as in Fig. 3, but for the set of three DM solitons, with β ¯ = 0.2 and peak powers { P 1 P 2 P 1 } . Here is shown an example with P 1 = 1.51 and P 2 = 0.91 , the widths and values of the DM strength of the respective DM solitons being ( T FWHM ) 1 = 1.44 , S 1 = 0.96 , and ( T FWHM ) 2 = 1.66 , S 2 = 0.73 . Actually, the soliton with peak power P 1 is the same as the soliton with the fixed power in Fig. 5.

Fig. 9
Fig. 9

The same as in Fig. 5a, but for the soliton triplets, { P 1 P 2 P 1 } , with fixed P 1 and varying P 2 . The soliton with the fixed parameters is the same as its counterpart in Fig. 8.

Equations (8)

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i u z 1 2 β ( z ) 2 u τ 2 + | u | 2 u = 0 ,
β ( z ) = β ¯ + { β , 0 < z < L , β + , L < z < L + L + . }
L = 1 , | β | L = β + L + = 1 .
u 0 ( τ ) = A 0 exp ( a 0 τ 2 2 ) ,
S = [ | β ¯ + β | L + ( β ¯ + β + ) L + ] T FWHM 2 2 T FWHM 2 ,
( T FWHM ) max ( T FWHM ) min = 1 + ( 2 ln 2 ) 2 S 2 ,
E = π ( 2 ln 2 S ) P .
4.5 < Δ T < 5.5 or 5.5 < Δ T < 6.5 ,

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