On a novel integrable generalization of the nonlinear Schrödinger equation

Abstract

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.

20 pages, 1 figure

References in corpus (2)

• An integrable shallow water equation with peaked solitons
• Exactly solvable model for nonlinear pulse propagation in optical fibers

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