Open AccessAsymptotical analysis of generalized Hirota–Satsuma type system
Author(s) -
Rima Kriauzienė,
Aleksandras Krylovas
Publication year - 2010
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2010.09
Subject(s) - nonlinear system , type (biology) , asymptotic analysis , mathematics , mathematical analysis , resonance (particle physics) , traveling wave , korteweg–de vries equation , nonlinear resonance , physics , geology , paleontology , particle physics , quantum mechanics
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.