On a novel integrable generalization of the nonlinear Schrödinger equation

Details On a novel integrable generalization of the nonlinear Schrödinger equation On a novel integrable generalization of the nonlinear Schrödinger equation

2008-12-08

arxiv.org/abs/0812.1510v1

Nonlinearity 22 (2009), 11--27

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, 1 figure

Scientific paper

10.1088/0951-7715/22/1/002

We consider an integrable generalization of the nonlinear Schr\"odinger (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 that 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. (d) Analyze solitons.

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