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Asymptotical analysis of some coupled nonlinear wave equations

    Aleksandras Krylovas Affiliation
    ; Rima Kriauzienė Affiliation

Abstract

We consider coupled nonlinear equations modelling a family of travelling wave solutions. The goal of our work is to show that the method of internal averaging along characteristics can be used for wide classes of coupled non-linear wave equations such as Korteweg-de Vries, Klein – Gordon, Hirota – Satsuma, etc. The asymptotical analysis reduces a system of coupled non-linear equations to a system of integro – differential averaged equations. The averaged system with the periodical initial conditions disintegrates into independent equations in non-resonance case. These equations describe simple weakly non-linear travelling waves in the non-resonance case. In the resonance case the integro – differential averaged systems describe interaction of waves and give a good asymptotical approximation for exact solutions.

Keyword : Non-linear waves, resonances, averaging, asymptotical integration

How to Cite
Krylovas, A., & Kriauzienė, R. (2011). Asymptotical analysis of some coupled nonlinear wave equations. Mathematical Modelling and Analysis, 16(1), 97-108. https://doi.org/10.3846/13926292.2011.560618
Published in Issue
Apr 8, 2011
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