Abstract. In this paper, we study the Vakhnenko equation with linear dissipation, which can be derived from the evolution of shallow water waves on a rotating fluid in the limit of small high-frequency dissipation. We show that the wave breaking phenomenon is affected by the dissipative parameters, we also determine the exact blow-up rate of wave breaking solutions.

Received: December 13, 2013

AMS Subject Classification: 35G25, 35L05, 35B30, 35L55

Key Words and Phrases: Vakhnenko equation, wave breaking

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