WKB analysis for the three coupled long wave–short wave interaction equations. Issue 9 (3rd July 2020)

• Record Type: Journal Article
• Authors: Muslu, Gulcin M.; Lin, Chi-Kun
• Is Part Of: Applicable analysis. Volume 99:Issue 9(2020)
• Page Start: 1507
• Page End: 1527
• Publication Date: 2020-07-03
• Subjects: WKB analysis -- long wave -- short wave -- dispersive perturbation -- quasilinear hyperbolic system -- split-step Fourier method; 81Q20 -- 35A01 -- 35L45 -- 35Q35 -- 65M70; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1538503
• Languages: English
• ISSNs: 0003-6811

Abstract

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.