On a novel integrable generalization of the nonlinear Schrödinger equation

By Jonatan Lenells, A. S. Fokas. 2008

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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 as 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 and (d) analyse solitons.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a8f9684fb621f5c6eca3c9d7730a0d3b117a3c67