Asymptotical analysis of some coupled nonlinear wave equations

A. Krylovas, R. Kriauziene

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider coupled nonlinear equations modelling a family of traveling wave solutions. The goal of our work is to show that the method of internal averaging along characteristics can be used for wide classes of coupled non-linear wave equations such as Korteweg-de Vries, Klein - Gordon, Hirota - Satsuma, etc. The asymptotical analysis reduces a system of coupled non-linear equations to a system of integro - differential averaged equations. The averaged system with the periodical initial conditions disintegrates into independent equations in non-resonance case. These equations describe simple weakly non-linear travelling waves in the non-resonance case. In the resonance case the integro - differential averaged systems describe interaction of waves and give a good asymptotical approximation for exact solutions.

Original languageEnglish
Pages (from-to)97-108
Number of pages12
JournalMathematical Modelling and Analysis
Volume16
Issue number1
DOIs
Publication statusPublished - Mar 2011
Externally publishedYes

Fingerprint

Nonlinear Wave Equation
Wave equations
Nonresonance
Nonlinear equations
Nonlinear Equations
Integrodifferential equations
Nonlinear Waves
Traveling Wave Solutions
Differential System
Integro-differential Equation
Traveling Wave
Averaging
Initial conditions
Exact Solution
Internal
Approximation
Interaction
Modeling

Keywords

  • Asymptotical integration
  • Averaging
  • Non-linear waves
  • Resonances

ASJC Scopus subject areas

  • Analysis
  • Modelling and Simulation

Cite this

Asymptotical analysis of some coupled nonlinear wave equations. / Krylovas, A.; Kriauziene, R.

In: Mathematical Modelling and Analysis, Vol. 16, No. 1, 03.2011, p. 97-108.

Research output: Contribution to journalArticle

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