P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 59, 1288–1302 (1999).

[CrossRef]

H. Sugahara, K. Hiroki, I. Takashi, 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]

J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, “Hamiltonian dynamics of dispersion-managed breathers,” J. Opt. Soc. Am. B 15, 87–96 (1998).

[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary propagations in the strong dispersion management limit,” Opt. Commun. 149, 366–375 (1998).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

F. Kh. Abdullaev and J. G. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).

[CrossRef]

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171–175 (1997).

[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).

[CrossRef]

B. A. Malomed, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).

[CrossRef]

N. J. Smith and N. J. Doran, “Picosecond soliton transmis-sion using concatenated nonlinear optical loop-mirror intensity filters,” J. Opt. Soc. Am. B 12, 1117–1125 (1995).

[CrossRef]

R.-J. Essiambre and G. P. Agrawal, “Soliton communication beyond the average-soliton regime,” J. Opt. Soc. Am. B 12, 2420–2425 (1995).

[CrossRef]

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun. 117, 65–70 (1995).

[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).

[CrossRef]

B. A. Malomed, “Bound states of envelope solitons,” Phys. Rev. E 47, 2874–2880 (1993).

[CrossRef]

M. Nakazawa, Y. Kimura, and K. Suzuki, “Soliton amplification and transmission with Er^{3+}-doped fibre repeater pumped by GaInAsP laser diode,” Electron. Lett. 25, 199–200 (1989).

[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).

[CrossRef]

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).

[CrossRef]

B. V. Chirikov, “A universal instability of many-dimensional oscillator systems,” Phys. Rep. 52, 263–379 (1979).

[CrossRef]

A. Bondeson, M. Lisak, and D. Andersen, “Soliton perturbations: a variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).

[CrossRef]

F. Kh. Abdullaev and J. G. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).

[CrossRef]

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171–175 (1997).

[CrossRef]

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171–175 (1997).

[CrossRef]

A. Bondeson, M. Lisak, and D. Andersen, “Soliton perturbations: a variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).

[CrossRef]

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171–175 (1997).

[CrossRef]

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun. 117, 65–70 (1995).

[CrossRef]

A. Bondeson, M. Lisak, and D. Andersen, “Soliton perturbations: a variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).

[CrossRef]

F. Kh. Abdullaev and J. G. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).

[CrossRef]

B. V. Chirikov, “A universal instability of many-dimensional oscillator systems,” Phys. Rep. 52, 263–379 (1979).

[CrossRef]

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun. 117, 65–70 (1995).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).

[CrossRef]

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).

[CrossRef]

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).

[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary propagations in the strong dispersion management limit,” Opt. Commun. 149, 366–375 (1998).

[CrossRef]

M. Nakazawa, Y. Kimura, and K. Suzuki, “Soliton amplification and transmission with Er^{3+}-doped fibre repeater pumped by GaInAsP laser diode,” Electron. Lett. 25, 199–200 (1989).

[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).

[CrossRef]

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun. 117, 65–70 (1995).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary propagations in the strong dispersion management limit,” Opt. Commun. 149, 366–375 (1998).

[CrossRef]

D. Anderson, M. Lisak, and T. Reichel, “Asymptotic propagation properties of pulses in a soliton-based optical-fiber communication system,” J. Opt. Soc. Am. B 5, 207–210 (1988).

[CrossRef]

A. Bondeson, M. Lisak, and D. Andersen, “Soliton perturbations: a variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).

[CrossRef]

B. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Prog. Opt. 43, 69 (2002).

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary propagations in the strong dispersion management limit,” Opt. Commun. 149, 366–375 (1998).

[CrossRef]

B. A. Malomed, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).

[CrossRef]

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).

[CrossRef]

B. A. Malomed, “Resonant transmission of a chirped soliton in a long optical fiber with periodic amplification,” J. Opt. Soc. Am. B 13, 677–686 (1996).

[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).

[CrossRef]

B. A. Malomed, “Bound states of envelope solitons,” Phys. Rev. E 47, 2874–2880 (1993).

[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

M. Nakazawa, Y. Kimura, and K. Suzuki, “Soliton amplification and transmission with Er^{3+}-doped fibre repeater pumped by GaInAsP laser diode,” Electron. Lett. 25, 199–200 (1989).

[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).

[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

M. Nakazawa, Y. Kimura, and K. Suzuki, “Soliton amplification and transmission with Er^{3+}-doped fibre repeater pumped by GaInAsP laser diode,” Electron. Lett. 25, 199–200 (1989).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).

[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary propagations in the strong dispersion management limit,” Opt. Commun. 149, 366–375 (1998).

[CrossRef]

M. Nakazawa, Y. Kimura, and K. Suzuki, “Soliton amplification and transmission with Er^{3+}-doped fibre repeater pumped by GaInAsP laser diode,” Electron. Lett. 25, 199–200 (1989).

[CrossRef]

R.-J. Essiambre and G. P. Agrawal, “Soliton communication beyond the average-soliton regime,” J. Opt. Soc. Am. B 12, 2420–2425 (1995).

[CrossRef]

Y. Kominis and K. Hizanidis, “Regular and chaotic dynamics of periodically amplified picosecond solitons,” J. Opt. Soc. Am. B 19, 1746–1758 (2002).

[CrossRef]

Z. M. Liao, C. J. McKinstrie, and G. P. Agrawal, “Importance of prechirping in constant-dispersion fiber links with a large amplifier spacing,” J. Opt. Soc. Am. B 17, 514–518 (2000).

[CrossRef]

D. Anderson, M. Lisak, and T. Reichel, “Asymptotic propagation properties of pulses in a soliton-based optical-fiber communication system,” J. Opt. Soc. Am. B 5, 207–210 (1988).

[CrossRef]

N. J. Smith and N. J. Doran, “Picosecond soliton transmis-sion using concatenated nonlinear optical loop-mirror intensity filters,” J. Opt. Soc. Am. B 12, 1117–1125 (1995).

[CrossRef]

B. A. Malomed, “Resonant transmission of a chirped soliton in a long optical fiber with periodic amplification,” J. Opt. Soc. Am. B 13, 677–686 (1996).

[CrossRef]

J. N. Kutz, P. Holmes, S. G. Evangelides, and J. P. Gordon, “Hamiltonian dynamics of dispersion-managed breathers,” J. Opt. Soc. Am. B 15, 87–96 (1998).

[CrossRef]

S. K. Turitsyn, I. Gabitov, E. W. Laedke, V. K. Mezentsev, S. L. Musher, E. G. Shapiro, T. Schäfer, and K. H. Spatschek, “Variational approach to optical pulse propagation in dispersion-compensated transmission systems,” Opt. Commun. 151, 117–135 (1998).

[CrossRef]

B. A. Malomed, “Pulse propagation in a nonlinear optical fiber with periodically modulated dispersion: variational approach,” Opt. Commun. 136, 313–319 (1997).

[CrossRef]

T. I. Lakoba, J. Yang, D. J. Kaup, and B. A. Malomed, “Conditions for stationary propagations in the strong dispersion management limit,” Opt. Commun. 149, 366–375 (1998).

[CrossRef]

W. Forysiak, N. J. Doran, F. M. Knox, and K. J. Blow, “Average soliton dynamics in strongly perturbed systems,” Opt. Commun. 117, 65–70 (1995).

[CrossRef]

B. V. Chirikov, “A universal instability of many-dimensional oscillator systems,” Phys. Rep. 52, 263–379 (1979).

[CrossRef]

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).

[CrossRef]

I. Gabitov, E. G. Shapiro, and S. K. Turitsyn, “Asymptotic breathing pulse in optical transmission systems with dispersion compensation,” Phys. Rev. E 55, 3624–3633 (1997).

[CrossRef]

F. Kh. Abdullaev and J. G. Caputo, “Validation of the variational approach for chirped pulses in fibers with periodic dispersion,” Phys. Rev. E 58, 6637–6648 (1998).

[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, “Resonant shape oscillations and decay of a soliton in a periodically inhomogeneous nonlinear optical fiber,” Phys. Rev. E 48, 1418–1425 (1993).

[CrossRef]

B. A. Malomed, “Bound states of envelope solitons,” Phys. Rev. E 47, 2874–2880 (1993).

[CrossRef]

A. Bondeson, M. Lisak, and D. Andersen, “Soliton perturbations: a variational principle for the soliton parameters,” Phys. Scr. 20, 479–485 (1979).

[CrossRef]

R. Grimshaw, J. He, and B. A. Malomed, “Decay of a fundamental soliton in a periodically modulated nonlinear waveguide,” Phys. Scr. 53, 385–393 (1996).

[CrossRef]

B. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Prog. Opt. 43, 69 (2002).

F. Kh. Abdullaev, A. A. Abdumalikov, and B. B. Baizakov, “Stochastic instability of chirped optical solitons in media with periodic amplification,” Quantum Electron. 27, 171–175 (1997).

[CrossRef]

Y. S. Kivshar and B. A. Malomed, “Dynamics of solitons in nearly integrable systems,” Rev. Mod. Phys. 61, 763–915 (1989).

[CrossRef]

P. Holmes and J. N. Kutz, “Dynamics and bifurcations of a planar map modeling dispersion managed breathers,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 59, 1288–1302 (1999).

[CrossRef]

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, UK, 1995).

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980).

A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983).