Exactly solvable model for nonlinear pulse propagation in optical fibers

Details Exactly solvable model for nonlinear pulse propagation in optical fibers Exactly solvable model for nonlinear pulse propagation in optical fibers

2008-10-29

arxiv.org/abs/0810.5289v1

Physics

Optics

14 pages

Scientific paper

The nonlinear Schr\"odinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of bi-Hamiltonian methods in [A. S. Fokas, {\it Phys. D} {\bf 87} (1995), 145--150]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as a model for nonlinear pulse propagation in monomode optical fibers when certain higher-order nonlinear effects are taken into account; (b) We show that the equation is equivalent, up to a simple change of variables, to the first negative member of the integrable hierarchy associated with the derivative nonlinear Schr\"odinger equation; (c) We analyze traveling-wave solutions.

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