On a novel integrable generalization of the nonlinear Schr\"odinger equation
Exactly Solvable and Integrable Systems
2008-12-09 v1 Pattern Formation and Solitons
Abstract
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.
Cite
@article{arxiv.0812.1510,
title = {On a novel integrable generalization of the nonlinear Schr\"odinger equation},
author = {J. Lenells and A. S. Fokas},
journal= {arXiv preprint arXiv:0812.1510},
year = {2008}
}
Comments
20 pages, 1 figure