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

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

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