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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 9
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Articles

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

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Pages 1507-1527 | Received 26 Jul 2018, Accepted 13 Oct 2018, Published online: 02 Nov 2018
 

ABSTRACT

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.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Acknowledgements

The authors gratefully acknowledge to the anonymous reviewers for valuable suggestions. Part of this work was done when C.-K. Lin visited NCTS in Taiwan, he would like to thank their support and hospitality during his visit.

Disclosure statement

No potential conflict of interest was reported by the authors.

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