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On the initial-value problem to the Degasperis-Procesi equation with linear dispersion

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  • In this paper, we consider the initial-value problem for the Degasperis-Procesi equation with a linear dispersion, which is an approximation to the incompressible Euler equation for shallow water waves. We establish local well-posedness and some global existence of solutions for certain initial profiles and determine the wave breaking phenomena for the equation. Finally, we verify the occurrence of the breaking waves by numerical simulations.
    Mathematics Subject Classification: Primary: 35L30, 35L05; Secondary: 35L67.

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