Open AccessAsymptotic integration of systems of two wave equations with small parameter
Author(s) -
Aleksandras Krylovas
Publication year - 2016
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.b.2016.06
Subject(s) - nonlinear system , mathematics , mathematical analysis , homogeneous , series (stratigraphy) , perturbation (astronomy) , method of matched asymptotic expansions , scale (ratio) , asymptotic analysis , space (punctuation) , differential equation , physics , computer science , paleontology , quantum mechanics , operating system , combinatorics , biology
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.