Asymptotic integration of systems of two wave equations with small parameter
Articles
Aleksandras Krylovas
Vilniaus Gedimino technikos universitetas
Published 2016-12-20
https://doi.org/10.15388/LMR.B.2016.06
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Keywords

asymptotic solutions
averaging
wave equation
resonances

How to Cite

Krylovas A. (2016) “Asymptotic integration of systems of two wave equations with small parameter”, Lietuvos matematikos rinkinys, 57(B), pp. 31–36. doi: 10.15388/LMR.B.2016.06.

Abstract

In this article we consider a hyperbolic system of two weakly nonlinear equations. Coefficients of the equations and initial conditions are periodical functions of the space variable. A multi-scale perturbation technique and integrating along characteristics are used to construct asymptotic series without secular members. The scheme of asymptotic integration is applied to analysis of oscillations of nonlinear non-homogeneous strings.

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