Exactly solvable model for nonlinear pulse propagation in optical fibers

2008/10/29 by Lenells, Jonatan · 3 citations
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Optics (physics.optics)

paper · doi:10.48550/arxiv.0810.5289

Abstract

The nonlinear Schrödinger (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 Schrödinger equation; (c) We analyze traveling-wave solutions.

Cited by

• Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities
• A vectorial Darboux transformation for integrable matrix versions of the Fokas-Lenells equation
• Nonlocal massive Thirring model and its solutions

Related

• A Study of a Nonlinear Schrödinger Equation for Optical Fibers
• New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation
• Conservation laws, exact travelling waves and modulation instability for an extended nonlinear Schrödinger equation
• A Variational Approach in the Dissipative Nonlinear Schrödinger Equation
• Exact solutions to the nonlinear Schrödinger equation with time-dependent coefficients