On a novel integrable generalization of the nonlinear Schrodinger equation

被引：144

作者：

Lenells, J. ^{[1
]}

Fokas, A. S. ^{[1
]}

机构：

[1] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

来源：

NONLINEARITY | 2009年 / 22卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

SHALLOW-WATER EQUATION; CAMASSA-HOLM EQUATION; HEREDITARY SYMMETRIES; PEAKED SOLITONS;

D O I：

10.1088/0951-7715/22/1/002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an integrable generalization of the nonlinear Schrodinger (NLS) equation that was recently derived by one of the authors using bi-Hamiltonian methods. This equation is related to the NLS equation in the same way as the Camassa-Holm equation is related to the KdV equation. In this paper we (a) use the bi-Hamiltonian structure to write down the first few conservation laws, (b) derive a Lax pair, (c) use the Lax pair to solve the initial value problem and (d) analyse solitons.

引用

页码：11 / 27

页数：17

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