Application of the method of stationary phase to asymptotic integration of weakly nonlinear hyperbolic systems
Krylovas, Aleksandras | Vilniaus Gedimino technikos universitetas |
Hyperbolic weakly nonlinear system with periodical initial conditions is considered in the article. The unperturbated system describes non interacted travelling waves. Perturbated system describes some interaction of the waves, which can be complicated by resonances. The asymptotic solution of the problem can be nds as a solution of system, averaging along characteristics. The characteristics of system depend from slowly time and the problem of asymptotic substantiation is more di cult compare with constant characteristics case. This substantiation was makes in early work of the author for one class of solutions. In this article other class of solutions is considered and the other technics (method of stationary phase) is used to substantiate the asymptotic.