Explicit solutions of the Camassa-Holm equation

E.J. Parkes; V.O. Vakhnenko

doi:10.1016/j.chaos.2005.03.011

Explicit solutions of the Camassa-Holm equation

E.J. Parkes, V.O. Vakhnenko

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

Abstract

Explicit travelling-wave solutions of the Camassa-Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis-Procesi equation are given in an appendix.

Original language	English
Pages (from-to)	1309-1316
Number of pages	7
Journal	Chaos, Solitons and Fractals
Volume	26
Issue number	5
DOIs	https://doi.org/10.1016/j.chaos.2005.03.011
Publication status	Published - Dec 2005

Keywords

Camassa–Holm equation
solitons
finite element analysis
numerical mathematics

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10.1016/j.chaos.2005.03.011

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AU - Vakhnenko, V.O.

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AB - Explicit travelling-wave solutions of the Camassa-Holm equation are sought. The solutions are characterized by two parameters. For propagation in the positive x-direction, both periodic and solitary smooth-hump, peakon, cuspon and inverted-cuspon waves are found. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. Some composite wave solutions of the Degasperis-Procesi equation are given in an appendix.

KW - Camassa–Holm equation

KW - solitons

KW - finite element analysis

KW - numerical mathematics

UR - http://www.maths.strath.ac.uk/~caas35/p&vCSF05.pdf

UR - http://dx.doi.org/10.1016/j.chaos.2005.03.011

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M3 - Article

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EP - 1316

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 5

ER -

Explicit solutions of the Camassa-Holm equation

Abstract

Keywords

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