An equation unifying both Camassa-Holm and Novikov equations

Priscila Leal da  Silva; Igor Leite  Freire

doi:10.3934/proc.2015.0304

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2015, Volume 2015: 304-311. Doi: 10.3934/proc.2015.0304 open access

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An equation unifying both Camassa-Holm and Novikov equations

Priscila Leal da Silva^1, and
Igor Leite Freire^1,

1.
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC - UFABC, Rua Santa Adélia, 166, Bairro Bangu, 09.210 -- 170, Santo André, SP

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

In this paper we derive a new equation unifying the Camassa-Holm and Novikov equations invariant under the scaling transformation $(x,t,u)\mapsto(x,\lambda^{-b}t,\lambda u)$ and admitting a certain multiplier.

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Mathematics Subject Classification: Primary: 76M60, 58J70, 35A30, 70G65.

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