The study on solutions to Camassa-Holm equation with weak dissipation

Danping Ding; Lixin Tian; Gang Xu

doi:10.3934/cpaa.2006.5.483

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2006, Volume 5, Issue 3: 483-492. Doi: 10.3934/cpaa.2006.5.483

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The study on solutions to Camassa-Holm equation with weak dissipation

1.
Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013

Received: May 2005

Revised: February 2006

Published: September 2006

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Abstract

This paper investigates the existence of solution on the weak dissipative Camassa-Holm equation, and studies the dynamical behaviors of the solution for this equation. An interesting result is given that the solution for the Cauchy problem on weak dissipative Camassa-Holm equation is local under certain conditions. Moreover, discussions on solitary solution to weak dissipation Camassa-Holm equation are given.

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Mathematics Subject Classification: 35A07, 35B10, 35B45, 35L05.

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