Asymptotical analysis of generalized Hirota–Satsuma type system
Articles
Rima Kriauzienė
Mykolo Romerio universitetas
Aleksandras Krylovas
Vilniaus Gedimino technikos universitetas
Published 2010-12-21
https://doi.org/10.15388/LMR.2010.09
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Keywords

Hirota–Satsuma system
asymptotical analysis
averaging
interaction of waves

How to Cite

Kriauzienė R. and Krylovas A. (2010) “Asymptotical analysis of generalized Hirota–Satsuma type system”, Lietuvos matematikos rinkinys, 51(proc. LMS), pp. 51–56. doi: 10.15388/LMR.2010.09.

Abstract

Paper deals with the nonlinear coupled equations of the well known in the literature Hirota–Satsuma type system. The asymptotic analysis of this system, which is based on the principle of two scales and on averaging of weakly nonlinear hyperbolic systems along characteristics is presented in the paper. The asymptotic analysis shown that the system disintegrates on three independent Korteweg–de Vries equations in the non-resonance case, and the system describes an interaction of periodical nonlinear waves in the resonance case.

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