A numerical study of the semi-classical limit for three-coupled long wave–short wave interaction equations

Goksu Oruc; Emine Kesici; Gulcin M. Muslu

doi:10.1002/num.22335

A numerical study of the semi-classical limit for three-coupled long wave–short wave interaction equations

Goksu Oruc, Emine Kesici, Gulcin M. Muslu^*

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Technical University

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	993-1007
Number of pages	15
Journal	Numerical Methods for Partial Differential Equations
Volume	35
Issue number	3
DOIs	https://doi.org/10.1002/num.22335
Publication status	Published - May 2019

Bibliographical note

Publisher Copyright:
© 2018 Wiley Periodicals, Inc.

Funding

The first and the third authors (NS) acknowledge the support provided by the Research Fund of the Istanbul Technical University, 40655.

Funders	Funder number
Istanbul Teknik Üniversitesi	40655

Keywords

long wave–short wave interaction equations
meshing strategy
semi-classical limit
semi-discrete scheme
split-step Fourier method

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10.1002/num.22335

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abstract = "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.",

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AU - Oruc, Goksu

AU - Kesici, Emine

AU - Muslu, Gulcin M.

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

KW - long wave–short wave interaction equations

KW - meshing strategy

KW - semi-classical limit

KW - semi-discrete scheme

KW - split-step Fourier method

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JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 3

ER -

A numerical study of the semi-classical limit for three-coupled long wave–short wave interaction equations

Abstract

Bibliographical note

Funding

Keywords

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