Soliton scattering from a finite cnoidal wave train in a fiber

H. J. Shin

doi:10.1103/PhysRevE.63.026606

Access by Xinjiang University

Soliton scattering from a finite cnoidal wave train in a fiber

H. J. Shin^*

Department of Physics and Research Institute of Basic Sciences, Kyunghee University, Seoul 130-701, Korea

^*Email address; hjshin@khu.ac.kr

PDF

Phys. Rev. E 63, 026606 – Published 22 January, 2001

DOI: https://doi.org/10.1103/PhysRevE.63.026606

Abstract

We analyze the scattering of a soliton from a cnoidal wave train in a fiber theoretically as well as numerically. Solitons recover their original shapes and velocities after collisions, while shapes of cnoidal waves are nearly preserved during collisions. The effect of collisions is described by the change of velocities of solitons, and the theoretical predictions are in good agreement with numerical results.

References (13)

See, for example, M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge University Press, New York, 1992), and references therein.
C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).
E. Fredkin and T. Toffoli, Int. J. Theor. Phys. 21, 219 (1982).
A. Hasegawa and Y. Kodama, Opt. Lett. 7, 285 (1982).
B. Jaskorzynska and D. Schadt, IEEE J. Quantum Electron. 24, 2117 (1988); E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, Opt. Lett. 15, 851 (1990).
Q-H. Park and H. J. Shin, Phys. Rev. Lett. 82, 4432 (1999).
J. Mertsching, Fortschr. Phys. 35, 519 (1987).
Encyclopedic Dictionary of Mathematics, edited by K. Itô (MIT Press, Cambridge, MA, 1993).
F. Abdullaev, S. Darmanyan and P. Khabibullaev, Optical Solitons, Springer Series in Nonlinear Dynamics (Springer-Verlag, Heidelberg, 1993); their solutions through the Riemann surface have a rather complicated form that prevents their applications to real physical situations; see also, A. Kamchatnov, Phys. Rep. 286, 199 (1997).
Q-H. Park and H. J. Shin, Phys. Rev. A 57, 4621 (1998); ibid.57, 4643 (1998); Phys. Rev. E 61, 3093 (2000); Opt. Commun. 178, 233 (2000).
A. Sym, Fluid Dyn. Res. 3, 151 (1988).
A simple MATHEMATICA program for the velocity is available from the author.
Like in Ref. [6], we use the effective time interval $D_{eff} = 0.87 Δ \bar{z}, 2 \vec{D} 2 D + 0.13 Δ z$ due to the rapid round off of square pulse edges of the CNW train.

[c1] See, for example, M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge University Press, New York, 1992), and references therein.

[c2] C. R. Menyuk, Opt. Lett. 12, 614 (1987); J. Opt. Soc. Am. B 5, 392 (1988).

[c3] E. Fredkin and T. Toffoli, Int. J. Theor. Phys. 21, 219 (1982).

[c4] A. Hasegawa and Y. Kodama, Opt. Lett. 7, 285 (1982).

[c5] B. Jaskorzynska and D. Schadt, IEEE J. Quantum Electron. 24, 2117 (1988); E. J. Greer, D. M. Patrick, P. G. J. Wigley, and J. R. Taylor, Opt. Lett. 15, 851 (1990).

[c6] Q-H. Park and H. J. Shin, Phys. Rev. Lett. 82, 4432 (1999).

[c7] J. Mertsching, Fortschr. Phys. 35, 519 (1987).

[c8] Encyclopedic Dictionary of Mathematics, edited by K. Itô (MIT Press, Cambridge, MA, 1993).

[c9] F. Abdullaev, S. Darmanyan and P. Khabibullaev, Optical Solitons, Springer Series in Nonlinear Dynamics (Springer-Verlag, Heidelberg, 1993); their solutions through the Riemann surface have a rather complicated form that prevents their applications to real physical situations; see also, A. Kamchatnov, Phys. Rep. 286, 199 (1997).

[c10] Q-H. Park and H. J. Shin, Phys. Rev. A 57, 4621 (1998); ibid.57, 4643 (1998); Phys. Rev. E 61, 3093 (2000); Opt. Commun. 178, 233 (2000).

[c11] A. Sym, Fluid Dyn. Res. 3, 151 (1988).

[c12] A simple MATHEMATICA program for the velocity is available from the author.

[c13] Like in Ref. [6], we use the effective time interval $D_{eff} = 0.87 Δ \bar{z}, 2 \vec{D} 2 D + 0.13 Δ z$ due to the rapid round off of square pulse edges of the CNW train.

Physical Review E

Export citation

Export citation

Soliton scattering from a finite cnoidal wave train in a fiber

Abstract

References (13)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation