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Exactly Solvable Model for Nonlinear Pulse Propagation in Optical Fibers
Author(s) -
Lenells Jonatan
Publication year - 2009
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2009.00454.x
Subject(s) - integrable system , nonlinear system , nonlinear schrödinger equation , hamiltonian (control theory) , mathematical analysis , mathematics , pulse (music) , schrödinger equation , physics , mathematical physics , quantum mechanics , mathematical optimization , voltage
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 [1]. 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 NLS equation; (c) We analyze traveling‐wave solutions.