On a Nonlinear Problem of the Breaking Water Waves

The paper is devoted to the initial boundary value problem for the Korteweg-de Vries-Benjamin-Bona-Mahony equation in a finite domain. This particular problem arises from the phenomenon of long wave with small amplitude in fluid. For certain initial-boundary problems for the Korteweg-de Vries-Benjamin-Bona-Mahony equation, we obtain the conditions of blowing-up of global and travelling wave solutions in finite time. The proof of the results is based on the nonlinear capacity method. In closing, we provide the exact and numerical examples.

Keywords

breaking waves; Korteweg-de Vries-Benjamin-Bona-Mahony equation; blow-up of solution; initial-boundary problems.

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