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Exact solutions for a higher-order nonlinear Schrödinger equation

Exact solutions for a higher-order nonlinear Schrödinger equation We performed a systematic analysis of exact solutions for the higher-order nonlinear Schrödinger equation i ψ X + ψ T T = a 1 ψ‖ψ ‖ 2 + a 2 ψ‖ψ ‖ 4 + ia 3 (ψ‖ψ ‖ 2 ) T +( a 4 + ia 5 )ψ(‖ψ ‖ 2 ) T that describes wave propagation in nonlinear dispersive media. The method consists of the determination of all transformations that reduce the equation to ordinary differential equations that are solved whenever possible. All obtained solutions fall into one of the following categories: ‘‘bright’’ or ‘‘dark’’ solitary waves, solitonic waves, regular and singular periodic waves, shock waves, accelerating waves, and self-similar solutions. They are expressed in terms of simple functions except for few cases given in terms of the less-known Painlevé transcendents. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Exact solutions for a higher-order nonlinear Schrödinger equation

Physical Review A , Volume 41 (8) – Apr 15, 1990
8 pages

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Publisher
American Physical Society (APS)
Copyright
Copyright © 1990 The American Physical Society
ISSN
1094-1622
DOI
10.1103/PhysRevA.41.4478
Publisher site
See Article on Publisher Site

Abstract

We performed a systematic analysis of exact solutions for the higher-order nonlinear Schrödinger equation i ψ X + ψ T T = a 1 ψ‖ψ ‖ 2 + a 2 ψ‖ψ ‖ 4 + ia 3 (ψ‖ψ ‖ 2 ) T +( a 4 + ia 5 )ψ(‖ψ ‖ 2 ) T that describes wave propagation in nonlinear dispersive media. The method consists of the determination of all transformations that reduce the equation to ordinary differential equations that are solved whenever possible. All obtained solutions fall into one of the following categories: ‘‘bright’’ or ‘‘dark’’ solitary waves, solitonic waves, regular and singular periodic waves, shock waves, accelerating waves, and self-similar solutions. They are expressed in terms of simple functions except for few cases given in terms of the less-known Painlevé transcendents.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Apr 15, 1990

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