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

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.

KEYWORDS:

• WKB analysis
• long wave
• short wave
• dispersive perturbation
• quasilinear hyperbolic system
• split-step Fourier method

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 81Q20
• 35A01
• 35L45
• 35Q35
• 65M70

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.