Abstract

A unified analytical description of the evolution of quasi-linear optical pulses and solitons in strongly dispersion-managed transmission systems is developed. Asymptotic analysis of the nonlocal equation that describes the averaged dynamics of a dispersion-managed system shows that the nonlinearity decreases for large map strength s, as Olog s/s. The spectral intensity is found to be an invariant of the propagation, which allows the phase shift to be computed. These findings provide a clear description of pulse propagation in the quasi-linear regime, which is characterized by much lower energies than those required for stable dispersion-managed soliton transmission with the same dispersion map.

© 2001 Optical Society of America

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    [CrossRef]
  2. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
    [CrossRef]
  3. V. E. Zakharov and S. Wabnitz, eds., Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1999).
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    [CrossRef]
  5. I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
    [CrossRef]
  6. M. J. Ablowitz, G. Biondini, and E. S. Olson, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.
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    [CrossRef]
  8. V. E. Zakharov, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabritz, eds. (Springer-Verlag, Berlin, 1999), pp. 73–89.
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    [CrossRef]
  10. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
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    [CrossRef]
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2000

R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper FC1.

M. J. Ablowitz and T. Hirooka, Opt. Lett. 25, 1750 (2000).
[CrossRef]

1999

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578 (1999).
[CrossRef]

P. V. Mamyshev and N. A. Mamysheva, Opt. Lett. 24, 1454 (1999).
[CrossRef]

1998

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
[CrossRef]

1996

1995

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

1993

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and T. Hirooka, Opt. Lett. 25, 1750 (2000).
[CrossRef]

M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
[CrossRef]

M. J. Ablowitz, G. Biondini, and E. S. Olson, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

Abramov, A. A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Alleston, S. B.

P. Harper, S. B. Alleston, D. S. Govan, W. Forysiak, I. Bennion, and N. J. Doran, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Bennion, I.

P. Harper, S. B. Alleston, D. S. Govan, W. Forysiak, I. Bennion, and N. J. Doran, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Bergano, N. S.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Berntson, A.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

Biondini, G.

M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
[CrossRef]

M. J. Ablowitz, G. Biondini, and E. S. Olson, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

Chraplyvy, A. R.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Corbett, P. C.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Darcie, J. M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Davidson, C. R.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Doran, N. J.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

P. Harper, S. B. Alleston, D. S. Govan, W. Forysiak, I. Bennion, and N. J. Doran, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Evangelides, S. G.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Forghieri, F.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Forysiak, W.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

P. Harper, S. B. Alleston, D. S. Govan, W. Forysiak, I. Bennion, and N. J. Doran, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Fujii, K.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Fukuchi, K.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Gabitov, I. R.

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Golovchenko, E.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Govan, D. S.

P. Harper, S. B. Alleston, D. S. Govan, W. Forysiak, I. Bennion, and N. J. Doran, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Grigoryan, V. S.

R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper FC1.

Harper, P.

P. Harper, S. B. Alleston, D. S. Govan, W. Forysiak, I. Bennion, and N. J. Doran, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Hasegawa, A.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Hirooka, T.

Inada, Y.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Ito, T.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Kakui, M.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Kidorf, H. D.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Kurtzke, C.

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

Ma, M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Mamyshev, P. V.

Mamysheva, N. A.

Manakov, S. V.

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578 (1999).
[CrossRef]

Menges, R.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Menyuk, C. R.

R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper FC1.

Mills, M. A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Mu, R.-M.

R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper FC1.

Nijhof, J. H. B.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

Olson, E. S.

M. J. Ablowitz, G. Biondini, and E. S. Olson, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

Peckham, D.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Pedersen, B.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Pillipetskii, A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Rottwitt, K.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Sasaki, A.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Shikii, S.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Shitomi, T.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Sugahara, H.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Tsuzaki, T.

K. Fukuchi, M. Kakui, A. Sasaki, T. Ito, Y. Inada, T. Tsuzaki, T. Shitomi, K. Fujii, S. Shikii, H. Sugahara, and A. Hasegawa, in 25th European Conference on Optical Communication (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), paper PD2–10.

Turitsyn, S. K.

Vengsarkar, A. M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Wabnitz, S.

V. E. Zakharov and S. Wabnitz, eds., Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1999).

Yu, T.

R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper FC1.

Zakharov, V. E.

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578 (1999).
[CrossRef]

V. E. Zakharov and S. Wabnitz, eds., Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1999).

V. E. Zakharov, in Optical Solitons: Theoretical Challenges and Industrial Perspectives, V. E. Zakharov and S. Wabritz, eds. (Springer-Verlag, Berlin, 1999), pp. 73–89.

1998 OSA Technical Digest Series

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

R.-M. Mu, T. Yu, V. S. Grigoryan, and C. R. Menyuk, in Optical Fiber Communication Conference, Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2000), paper FC1.

Electron. Lett.

J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett. 34, 481 (1998).
[CrossRef]

IEEE J. Lightwave Technol.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

JETP Lett.

V. E. Zakharov and S. V. Manakov, JETP Lett. 70, 578 (1999).
[CrossRef]

Opt. Lett.

Other

M. J. Ablowitz, G. Biondini, and E. S. Olson, in Massive WDM and TDM Soliton Transmission Systems, A. Hasegawa, ed. (Kluwer Academic, Dordrecht, The Netherlands, 2000), pp. 75–114.

V. E. Zakharov and S. Wabnitz, eds., Optical Solitons: Theoretical Challenges and Industrial Perspectives (Springer-Verlag, Berlin, 1999).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

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Figures (2)

Fig. 1
Fig. 1

Shape of the quasi-linear Gaussian pulse after a propagation of z=20 (solid curves) and the initial profile (dotted curves) for s=100, d=0, and Γ=0: (a) frequency domain, (b) time domain. In (a), the dotted curve is indistinguishable from the solid curve.

Fig. 2
Fig. 2

Nonlinear phase shift ϕNLω=0 of the quasi-linear Gaussian pulse with β=0.5, 1.0. The solid curve is the analytical result (see text), and the circles and crosses are the numerical results obtained from the direct simulation of Eq.  (1) with Γ=0 and Γ=10, respectively.

Equations (7)

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iuz+dz22ut2+gzu2u=0,
iU^z-d2ω2U^+IU^z,ω=0,
IU^z,ω=-+dω1dω2U^z,ω+ω1U^z,ω+ω2×U^*z,ω+ω1+ω2rω1ω2,
rx;s=12π2sinsxsx.
IU^z,ω=ΨU^z,ω2U^z,ω+O1/s2,
ΨU^z,ω2=12πslog s-γU^z,ω2--dωfω-ωU^z,ω2,
U^z,ω=U^0,ωexpidω2z/2+iΨU^0,ω2z.

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