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A numerical study of the semi‐classical limit for three‐coupled long wave–short wave interaction equations
Author(s) -
Oruc Goksu,
Kesici Emine,
Muslu Gulcin M.
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22335
Subject(s) - mathematics , limit (mathematics) , discretization , mathematical analysis , fourier transform , plane wave , space (punctuation) , galerkin method , gaussian , wave equation , discontinuous galerkin method , physics , finite element method , nonlinear system , quantum mechanics , linguistics , philosophy , thermodynamics
We study numerically the semi‐classical limit for three‐coupled long wave–short wave interaction equations. The Fourier–Galerkin semi‐discretization is proved to be spectrally convergent in an appropriate energy space. We propose a split‐step Fourier method in the semi‐classical regime with the discussion of the meshing strategy, which is necessary to obtain correct numerical solution. Plane wave solution with weak and strong initial phases, solitary wave solution and Gaussian solution are considered to investigate the semi‐classical limit.