# On a Nonlinear Problem of the Breaking Water Waves

M. Kirane, B.T. TorebekThe 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.Full text

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