On a novel integrable generalization of the nonlinear Schr\"odinger equation

A. S. Fokas; J. Lenells

On a novel integrable generalization of the nonlinear Schr\"odinger equation

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arxiv 0812.1510 v1 pith:YLLAVNNT submitted 2008-12-08 nlin.SI nlin.PS

J. Lenells , A. S. Fokas This is my paper · ORCID

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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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