On a Nonlinear Problem of the Breaking Water Waves

Université de La Rochelle, Mokhtar Kirane, Berikbol T. Torebek

2019

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DOI 10.14529/mmp190203

Data confidence 70 medium

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Abstract

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.