On a novel integrable generalization of the nonlinear Schrödinger equation

@inproceedings{Lenells2008OnAN,
title={On a novel integrable generalization of the nonlinear Schr{\"o}dinger equation},
author={Jonatan Lenells and A. S. Fokas},
year={2008}
}

We consider an integrable generalization of the nonlinear Schrödinger (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. AMS… CONTINUE READING