Abstract

We present a series of chirp-free and chirped analytical nonautonomous soliton solutions to the generalized nonlinear Schrödinger equation with distributed coefficients by Darboux transformation from a trivial seed. For a chirp-free nonautonomous soliton, the dispersion management term can change the motion of a nonautonomous soliton and does not affect its shape at all. Specifically, the classical optical soliton can be presented with a variable dispersion term and nonlinearity when there is no gain. For a chirped nonautonomous soliton, dispersion management can meanwhile affect the shape and motion of nonautonomous solitons. The periodic dispersion term can be used to control its “breathing” shape, and it does not affect the trajectory of a nonautonomous soliton center with a certain condition.

© 2011 Optical Society of America

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  1. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
    [CrossRef]
  2. A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–172 (1973).
    [CrossRef]
  3. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
    [CrossRef]
  4. H. G. Luo, D. Zhao, and X. G. He, “Exactly controllable transmission of nonautonomous optical solitons,” Phys. Rev. A 79, 063802 (2009).
    [CrossRef]
  5. L. F. Mollenauer and K. Smith, “Demonstration of soliton transmission over more than 4000kmin fiber with loss periodically compensated by Raman gain,” Opt. Lett. 13, 675–677 (1988).
    [CrossRef] [PubMed]
  6. M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
    [CrossRef]
  7. M. Senturion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
    [CrossRef]
  8. V. N. Serkin and A. Hasegawa, “Novel soliton solution of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
    [CrossRef] [PubMed]
  9. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102(2007),
    [CrossRef] [PubMed]
  10. V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous matter wave solitons near Feshbach resonance,” Phys. Rev. A 81, 023610 (2010).
    [CrossRef]
  11. V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
    [CrossRef] [PubMed]
  12. S. A. Ponomarenko and G. P. Agrawal, “Interactions of chirped and chirp-free similaritons in optical fiber amplifiers,” Opt. Express 15, 2963–2973 (2007).
    [CrossRef] [PubMed]
  13. V. I. Kruglov, A. C. Peacock, J. M. Dudley, and J. D. Harvey, “Self-similar propagation of higher-power parabolic pulse in optical fiber amplifiers,” Opt. Lett. 25, 1753–1755 (2000).
    [CrossRef]
  14. B. A. Malomed, Soliton Management in Periodic Systems, (Springer, 2006).
  15. D. J. Richardson, R. P. Chamberlin, L. Dong, and D. N. Payne, “High quality soliton loss-compensation in 38km dispersion-decreasing fibre,” Electron. Lett. 31, 1681–1682 (1995).
    [CrossRef]
  16. A. J. Stentz, R. Boyd, and A. F. Evans, “Dramatically improved transmission of ultrashort solitons through 40km of dispersion-decreasing fiber,” Opt. Lett. 20, 1770–1772 (1995).
    [CrossRef] [PubMed]
  17. D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
    [CrossRef]
  18. K. Suzuki, H. Kubota, A. Sahara, and M. Nakazawa, “640Gbit/s (40Gbit/s 16 channel) dispersion-managed DWDM soliton transmission over 1000km with spectral efficiency of 0.4bit/Hz,” Electron. Lett. 36, 443–445 (2000).
    [CrossRef]
  19. M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
    [CrossRef]
  20. L. F. Mollenauer, P. V. Mamyshev, J. Gripp, M. J. Neubelt, N. Mamysheva, L. Gruner-Nielsen, and T. Veng, “Demonstration of massive wavelength-division multiplexing over transoceanic distances by use of dispersion-managed solitons,” Opt. Lett. 25, 704–706 (2000).
    [CrossRef]
  21. G. P. Agrawal, Nonliear Fiber Optics, 3rd ed. (Academic, 2001).

2010 (1)

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous matter wave solitons near Feshbach resonance,” Phys. Rev. A 81, 023610 (2010).
[CrossRef]

2009 (1)

H. G. Luo, D. Zhao, and X. G. He, “Exactly controllable transmission of nonautonomous optical solitons,” Phys. Rev. A 79, 063802 (2009).
[CrossRef]

2007 (2)

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102(2007),
[CrossRef] [PubMed]

S. A. Ponomarenko and G. P. Agrawal, “Interactions of chirped and chirp-free similaritons in optical fiber amplifiers,” Opt. Express 15, 2963–2973 (2007).
[CrossRef] [PubMed]

2006 (1)

M. Senturion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

2003 (1)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

2000 (6)

K. Suzuki, H. Kubota, A. Sahara, and M. Nakazawa, “640Gbit/s (40Gbit/s 16 channel) dispersion-managed DWDM soliton transmission over 1000km with spectral efficiency of 0.4bit/Hz,” Electron. Lett. 36, 443–445 (2000).
[CrossRef]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
[CrossRef]

L. F. Mollenauer, P. V. Mamyshev, J. Gripp, M. J. Neubelt, N. Mamysheva, L. Gruner-Nielsen, and T. Veng, “Demonstration of massive wavelength-division multiplexing over transoceanic distances by use of dispersion-managed solitons,” Opt. Lett. 25, 704–706 (2000).
[CrossRef]

V. I. Kruglov, A. C. Peacock, J. M. Dudley, and J. D. Harvey, “Self-similar propagation of higher-power parabolic pulse in optical fiber amplifiers,” Opt. Lett. 25, 1753–1755 (2000).
[CrossRef]

V. N. Serkin and A. Hasegawa, “Novel soliton solution of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[CrossRef] [PubMed]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
[CrossRef]

1996 (1)

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

1995 (2)

D. J. Richardson, R. P. Chamberlin, L. Dong, and D. N. Payne, “High quality soliton loss-compensation in 38km dispersion-decreasing fibre,” Electron. Lett. 31, 1681–1682 (1995).
[CrossRef]

A. J. Stentz, R. Boyd, and A. F. Evans, “Dramatically improved transmission of ultrashort solitons through 40km of dispersion-decreasing fiber,” Opt. Lett. 20, 1770–1772 (1995).
[CrossRef] [PubMed]

1988 (1)

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

1973 (2)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–172 (1973).
[CrossRef]

Agrawal, G. P.

Belyaeva, T. L.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous matter wave solitons near Feshbach resonance,” Phys. Rev. A 81, 023610 (2010).
[CrossRef]

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102(2007),
[CrossRef] [PubMed]

Boyd, R.

Chamberlin, R. P.

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

D. J. Richardson, R. P. Chamberlin, L. Dong, and D. N. Payne, “High quality soliton loss-compensation in 38km dispersion-decreasing fibre,” Electron. Lett. 31, 1681–1682 (1995).
[CrossRef]

Dong, L.

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

D. J. Richardson, R. P. Chamberlin, L. Dong, and D. N. Payne, “High quality soliton loss-compensation in 38km dispersion-decreasing fibre,” Electron. Lett. 31, 1681–1682 (1995).
[CrossRef]

Dudley, J. M.

Ellis, A. D.

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

Evans, A. F.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Gripp, J.

Gruner-Nielsen, L.

Harvey, J. D.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, J. M. Dudley, and J. D. Harvey, “Self-similar propagation of higher-power parabolic pulse in optical fiber amplifiers,” Opt. Lett. 25, 1753–1755 (2000).
[CrossRef]

Hasegawa, A.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous matter wave solitons near Feshbach resonance,” Phys. Rev. A 81, 023610 (2010).
[CrossRef]

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102(2007),
[CrossRef] [PubMed]

V. N. Serkin and A. Hasegawa, “Novel soliton solution of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[CrossRef] [PubMed]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–172 (1973).
[CrossRef]

He, X. G.

H. G. Luo, D. Zhao, and X. G. He, “Exactly controllable transmission of nonautonomous optical solitons,” Phys. Rev. A 79, 063802 (2009).
[CrossRef]

Kevrekidis, P. G.

M. Senturion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Kruglov, V. I.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, J. M. Dudley, and J. D. Harvey, “Self-similar propagation of higher-power parabolic pulse in optical fiber amplifiers,” Opt. Lett. 25, 1753–1755 (2000).
[CrossRef]

Kubota, H.

K. Suzuki, H. Kubota, A. Sahara, and M. Nakazawa, “640Gbit/s (40Gbit/s 16 channel) dispersion-managed DWDM soliton transmission over 1000km with spectral efficiency of 0.4bit/Hz,” Electron. Lett. 36, 443–445 (2000).
[CrossRef]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
[CrossRef]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
[CrossRef]

Luo, H. G.

H. G. Luo, D. Zhao, and X. G. He, “Exactly controllable transmission of nonautonomous optical solitons,” Phys. Rev. A 79, 063802 (2009).
[CrossRef]

Malomed, B. A.

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

Mamyshev, P. V.

Mamysheva, N.

Mollenauer, L. F.

Nakazawa, M.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
[CrossRef]

K. Suzuki, H. Kubota, A. Sahara, and M. Nakazawa, “640Gbit/s (40Gbit/s 16 channel) dispersion-managed DWDM soliton transmission over 1000km with spectral efficiency of 0.4bit/Hz,” Electron. Lett. 36, 443–445 (2000).
[CrossRef]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
[CrossRef]

Neubelt, M. J.

Payne, D. N.

D. J. Richardson, R. P. Chamberlin, L. Dong, and D. N. Payne, “High quality soliton loss-compensation in 38km dispersion-decreasing fibre,” Electron. Lett. 31, 1681–1682 (1995).
[CrossRef]

Peacock, A. C.

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

V. I. Kruglov, A. C. Peacock, J. M. Dudley, and J. D. Harvey, “Self-similar propagation of higher-power parabolic pulse in optical fiber amplifiers,” Opt. Lett. 25, 1753–1755 (2000).
[CrossRef]

Pender, W. A.

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

Ponomarenko, S. A.

Porter, M. A.

M. Senturion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Psaltis, D.

M. Senturion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Richardson, D. J.

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

D. J. Richardson, R. P. Chamberlin, L. Dong, and D. N. Payne, “High quality soliton loss-compensation in 38km dispersion-decreasing fibre,” Electron. Lett. 31, 1681–1682 (1995).
[CrossRef]

Sahara, A.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
[CrossRef]

K. Suzuki, H. Kubota, A. Sahara, and M. Nakazawa, “640Gbit/s (40Gbit/s 16 channel) dispersion-managed DWDM soliton transmission over 1000km with spectral efficiency of 0.4bit/Hz,” Electron. Lett. 36, 443–445 (2000).
[CrossRef]

Sahata, A.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
[CrossRef]

Senturion, M.

M. Senturion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

Serkin, V. N.

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous matter wave solitons near Feshbach resonance,” Phys. Rev. A 81, 023610 (2010).
[CrossRef]

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102(2007),
[CrossRef] [PubMed]

V. N. Serkin and A. Hasegawa, “Novel soliton solution of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[CrossRef] [PubMed]

Smith, K.

Stentz, A. J.

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Suzuki, K.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
[CrossRef]

K. Suzuki, H. Kubota, A. Sahara, and M. Nakazawa, “640Gbit/s (40Gbit/s 16 channel) dispersion-managed DWDM soliton transmission over 1000km with spectral efficiency of 0.4bit/Hz,” Electron. Lett. 36, 443–445 (2000).
[CrossRef]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–172 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Veng, T.

Widdowson, T.

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

Yamada, E.

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
[CrossRef]

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
[CrossRef]

Zhao, D.

H. G. Luo, D. Zhao, and X. G. He, “Exactly controllable transmission of nonautonomous optical solitons,” Phys. Rev. A 79, 063802 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23, 171–172 (1973).
[CrossRef]

Chaos (1)

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahara, “Recent progress in soliton transmission technology,” Chaos 10, 486–514 (2000).
[CrossRef]

Electron. Lett. (3)

D. J. Richardson, L. Dong, R. P. Chamberlin, A. D. Ellis, T. Widdowson, and W. A. Pender, “Periodically amplified system based on loss compensating dispersion decreasing fibre,” Electron. Lett. 32, 373–378 (1996).
[CrossRef]

K. Suzuki, H. Kubota, A. Sahara, and M. Nakazawa, “640Gbit/s (40Gbit/s 16 channel) dispersion-managed DWDM soliton transmission over 1000km with spectral efficiency of 0.4bit/Hz,” Electron. Lett. 36, 443–445 (2000).
[CrossRef]

D. J. Richardson, R. P. Chamberlin, L. Dong, and D. N. Payne, “High quality soliton loss-compensation in 38km dispersion-decreasing fibre,” Electron. Lett. 31, 1681–1682 (1995).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Nakazawa, H. Kubota, K. Suzuki, E. Yamada, and A. Sahata, “Ultrahigh-speed long-distance TDM and WDM soliton transmission technologies,” IEEE J. Sel. Top. Quantum Electron. 6, 363–396 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (2)

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous matter wave solitons near Feshbach resonance,” Phys. Rev. A 81, 023610 (2010).
[CrossRef]

H. G. Luo, D. Zhao, and X. G. He, “Exactly controllable transmission of nonautonomous optical solitons,” Phys. Rev. A 79, 063802 (2009).
[CrossRef]

Phys. Rev. Lett. (5)

V. I. Kruglov, A. C. Peacock, and J. D. Harvey, “Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients,” Phys. Rev. Lett. 90, 113902 (2003).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

M. Senturion, M. A. Porter, P. G. Kevrekidis, and D. Psaltis, “Nonlinearity management in optics: experiment, theory, and simulation,” Phys. Rev. Lett. 97, 033903 (2006).
[CrossRef]

V. N. Serkin and A. Hasegawa, “Novel soliton solution of the nonlinear Schrödinger equation model,” Phys. Rev. Lett. 85, 4502–4505 (2000).
[CrossRef] [PubMed]

V. N. Serkin, A. Hasegawa, and T. L. Belyaeva, “Nonautonomous solitons in external potentials,” Phys. Rev. Lett. 98, 074102(2007),
[CrossRef] [PubMed]

Other (2)

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

G. P. Agrawal, Nonliear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (4)

Fig. 1
Fig. 1

Dynamics of the chirp-free bright temporal nonautonomous soliton under periodic dispersion management for α = 2 , l = 1 , ω = 2 , g = 0.25 , A c = 2 , β = 1 .

Fig. 2
Fig. 2

(a) Dynamics of the chirped bright nonautonomous soliton under periodic dispersion management for α = 2 , l = 3 , ω = 3 , g = 0.25 , A c = 1 , β = 1 , h = 5 . (b) Contour plot of (a) with the same parameters. It is obvious that the soliton is breathing, and both width and peak oscillate with time.

Fig. 3
Fig. 3

(a) Dynamics of chirped bright nonautonomous solitons under periodic dispersion management and A c = 8 , α = 2 , l = 3 , ω = 3 , g = 0.25 , β = 1 , h = 5 . (b) Contour plot with same parameters. It is obvious that the soliton is breathing, its width and peak oscillate with time, and its center oscillates also.

Fig. 4
Fig. 4

Dynamics of bright solitons under dispersion management Ω ( Z ) = l cos ( ω Z ) + l 0 . (a) l 0 = 0.03 , the nonautonomous soliton breathes more and more lightly; (b) l 0 = 0.03 , it breathes more and more heavily. The other coefficients are α = 2 , l = 3 , ω = 3 , A c = 1 , g = 0.25 , β = 1 , h = 5 .

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

i U Z + Ω ( Z ) 2 U T 2 + R ( Z ) | U | 2 U + i G ( Z ) 2 U = 0 ,
R ( Z ) = 2 g Ω ( Z ) exp [ G ( Z ) d Z ] ,
U ( τ , Z ) = Q ( T , Z ) exp [ G ( Z ) / 2 d Z ] ;
i Q Z + Ω ( Z ) Q T T + f ( Z ) T Q + 2 g Ω ( Z ) | Q | 2 Q = 0 ,
T ϕ = F ϕ ( T , Z ) , Z ϕ = W ϕ ( T , Z ) ,
F = ( ζ g Q g Q ¯ ζ ) , W = ( A B C A ) .
A = 2 i Ω ( Z ) ζ 2 + i g Ω ( Z ) | Q | 2 , B = 2 i g Ω ( Z ) Q ζ + i g Ω ( Z ) Q T , C = 2 i g Ω ( Z ) Q ¯ ζ + i g Ω ( Z ) Q ¯ T ,
U [ T , Z ] = 4 α A c exp θ g [ 1 + A c 2 exp φ ] ,
θ = 2 T ( α i β ) d Z G ( Z ) / 2 + i 4 ( α i β ) 2 d Z Ω ( Z ) φ = 16 α β d Z Ω ( Z ) 4 α T ,
T c = ln A c 2 α + 4 β Ω ( Z ) d Z .
W ( Z ) = 1 4 α ln 3 + 2 2 3 2 2 ,
| U | max 2 = 4 α 2 exp [ G ( Z ) d Z ] / | g | .
| U | 2 = 16 α 2 A c 2 exp [ φ G ( Z ) d Z ] g [ 1 + A c 2 exp φ ] 2 ,
U ( T , Z ) = 4 b ( Z ) A c exp [ θ ( T , Z ) ] g ( 1 + A c 2 exp [ φ ( T , Z ) ] ) ,
θ ( T , Z ) = 2 [ b ( Z ) i d ( Z ) ] T + i C 2 ( Z ) T 2 + [ G ( Z ) / 2 + 2 Ω ( Z ) C 2 ( Z ) ] d Z + 4 i Ω ( Z ) [ b ( Z ) i d ( Z ) ] 2 d Z , φ ( T , Z ) = 4 b ( Z ) T + 16 Ω ( Z ) b ( Z ) d ( Z ) d Z , b ( Z ) = α exp [ 4 Ω ( Z ) C 2 ( Z ) d Z ] , d ( Z ) = β exp [ 4 Ω ( Z ) C 2 ( Z ) d Z ] .
W ( Z ) = 1 4 b ( Z ) ln 3 + 2 2 3 2 2 .
| U | max 2 = 4 b ( Z ) 2 g exp [ 4 Ω ( Z ) C 2 ( Z ) G ( Z ) d Z ] .
T c ( Z ) = ln A c 2 b ( Z ) + 4 Ω ( Z ) b ( Z ) d ( Z ) d Z b ( Z ) .
T c ( Z ) = ( 4 l sin ( ω Z ) / ω + h ) ln A c 2 α β .
W ( Z ) = 4 l sin ( ω Z ) + ω h 4 α ω ln 3 + 2 2 3 2 2 ,
| U | max 2 = 4 α 2 ω g [ 4 l sin ( ω Z ) + ω h ] .

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