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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Wave Collision for the gKdV-4 equation. Asymptotic Approach

Discontinuity, Nonlinearity, and Complexity 6(1) (2017) 35--47 | DOI:10.5890/DNC.2017.03.004

Georgy Omel’yanov

Department of Mathematics, University of Sonora, Hermosillo, Sonora, Mexico

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We consider an approach which allows to describe uniformly in time the process of collision of solitary waves. Next we apply it to the KdV-type equation with nonlinearity u4 for three interacting waves assuming that all wave trajectories intersect at the same point. The constructed asymptotic solution satisfies the equation in a weak sense and it can be treated as a classical asymptotics in the sense that it satisfies some conservation and balance laws associated with the gKdV-4 equation. Results of numerical simulation confirm the theoretical conclusion about the elastic type of the wave interaction.


The research was supported by SEP-CONACYT under grant 178690 (Mexico).


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