WKB analysis for the three coupled long wave-short wave interaction equations

This paper is devoted to the WKB analysis of the three coupled long wave-short wave interaction (LSI for short) equations. We consider the zero-dispersion limit of the LSI for initial data with Sobolev regularity, before the shocks appear in the limit system. For the smooth solution, the limit syste...

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Published inApplicable analysis Vol. 99; no. 9; pp. 1507 - 1527
Main Authors Muslu, Gulcin M., Lin, Chi-Kun
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.07.2020
Taylor & Francis Ltd
Subjects
Computational fluid dynamics
Computer simulation
dispersive perturbation
long wave
Mathematical analysis
quasilinear hyperbolic system
short wave
split-step Fourier method
Wave interaction
WKB analysis
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Summary:This paper is devoted to the WKB analysis of the three coupled long wave-short wave interaction (LSI for short) equations. We consider the zero-dispersion limit of the LSI for initial data with Sobolev regularity, before the shocks appear in the limit system. For the smooth solution, the limit system is given by the two fluids equations. The split-step Fourier method is also employed to justify the numerical simulation of the small dispersion limit.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2018.1538503