Elsevier

Applied Mathematics Letters

Volume 92, June 2019, Pages 121-127
Applied Mathematics Letters

On Kupershmidt’s extended equation of dispersive water waves

https://doi.org/10.1016/j.aml.2019.01.012Get rights and content
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Abstract

An extended equation of dispersive water waves, proposed by Kupershmidt, is considered. By an ansatz on eigenfunctions of its recursion operator, a linear spectral problem, which turns to be type of the energy dependent Schrödinger, is constructed for the system. As by-products, modified systems are presented. Furthermore, a new bi-Hamiltonian system is obtained and shown to be related to a three component generalization of the Camassa–Holm equation under a Miura-type transformation.

Keywords

Recursion operator
Linear spectral problem
Miura-type transformation

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