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Nonlocal symmetries and conservation laws of nonlocal Camassa-Holm type equations

Nonlocal symmetries and conservation laws of nonlocal Camassa-Holm type equations The two-component μ-Camassa-Holm equation, the μ-Camassa-Holm equation and the modified μ-Camassa-Holm equation are three nonlocal integrable models. In this paper, it is shown that the two-component μ-Camassa-Holm equation and the μ-Camassa-Holm equation with a linear dispersion admit a kind of nonlocal symmetries, and the modified μ-Camassa-Holm equation does not have such kind of nonlocal symmetry. An number of conservation laws to the modified μ-Camassa-Holm equation and μ-Camassa-Holm equation are obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Nonlocal symmetries and conservation laws of nonlocal Camassa-Holm type equations

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-015-0509-x
Publisher site
See Article on Publisher Site

Abstract

The two-component μ-Camassa-Holm equation, the μ-Camassa-Holm equation and the modified μ-Camassa-Holm equation are three nonlocal integrable models. In this paper, it is shown that the two-component μ-Camassa-Holm equation and the μ-Camassa-Holm equation with a linear dispersion admit a kind of nonlocal symmetries, and the modified μ-Camassa-Holm equation does not have such kind of nonlocal symmetry. An number of conservation laws to the modified μ-Camassa-Holm equation and μ-Camassa-Holm equation are obtained.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Nov 3, 2015

References