Higher order dispersive effects in regularized Boussinesq equation

Goksu Oruc; Handan Borluk; Gulcin M. Muslu

doi:10.1016/j.wavemoti.2016.10.005

Higher order dispersive effects in regularized Boussinesq equation

Goksu Oruc, Handan Borluk^*, Gulcin M. Muslu

^*Corresponding author for this work

Department of Mathematics Engineering

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

7 Citations (Scopus)

Abstract

In this paper, we consider the higher order Boussinesq (HBq) equation which models the bi-directional propagation of longitudinal waves in various continuous media. The equation contains the higher order effects of frequency dispersion. The present study is devoted to the numerical investigation of the HBq equation. For this aim a numerical scheme combining the Fourier pseudo-spectral method in space and a Runge–Kutta method in time is constructed. The convergence of semi-discrete scheme is proved in an appropriate Sobolev space. To investigate the higher order dispersive effects and nonlinear effects on the solutions of HBq equation, propagation of single solitary wave, head-on collision of solitary waves and blow-up solutions are considered.

Original language	English
Pages (from-to)	272-282
Number of pages	11
Journal	Wave Motion
Volume	68
DOIs	https://doi.org/10.1016/j.wavemoti.2016.10.005
Publication status	Published - 1 Jan 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.

Funding

This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the project MFAG-113F114 . The authors gratefully acknowledge to the anonymous reviewers for the constructive comments and valuable suggestions which improved the first draft of paper.

Funders	Funder number
TUBITAK	MFAG-113F114
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu

Keywords

Blow-up
Fourier pseudo-spectral method
Head-on collision of solitary waves
Solitary waves
The higher-order Boussinesq equation

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10.1016/j.wavemoti.2016.10.005

Cite this

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title = "Higher order dispersive effects in regularized Boussinesq equation",

abstract = "In this paper, we consider the higher order Boussinesq (HBq) equation which models the bi-directional propagation of longitudinal waves in various continuous media. The equation contains the higher order effects of frequency dispersion. The present study is devoted to the numerical investigation of the HBq equation. For this aim a numerical scheme combining the Fourier pseudo-spectral method in space and a Runge–Kutta method in time is constructed. The convergence of semi-discrete scheme is proved in an appropriate Sobolev space. To investigate the higher order dispersive effects and nonlinear effects on the solutions of HBq equation, propagation of single solitary wave, head-on collision of solitary waves and blow-up solutions are considered.",

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AU - Oruc, Goksu

AU - Borluk, Handan

AU - Muslu, Gulcin M.

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N2 - In this paper, we consider the higher order Boussinesq (HBq) equation which models the bi-directional propagation of longitudinal waves in various continuous media. The equation contains the higher order effects of frequency dispersion. The present study is devoted to the numerical investigation of the HBq equation. For this aim a numerical scheme combining the Fourier pseudo-spectral method in space and a Runge–Kutta method in time is constructed. The convergence of semi-discrete scheme is proved in an appropriate Sobolev space. To investigate the higher order dispersive effects and nonlinear effects on the solutions of HBq equation, propagation of single solitary wave, head-on collision of solitary waves and blow-up solutions are considered.

AB - In this paper, we consider the higher order Boussinesq (HBq) equation which models the bi-directional propagation of longitudinal waves in various continuous media. The equation contains the higher order effects of frequency dispersion. The present study is devoted to the numerical investigation of the HBq equation. For this aim a numerical scheme combining the Fourier pseudo-spectral method in space and a Runge–Kutta method in time is constructed. The convergence of semi-discrete scheme is proved in an appropriate Sobolev space. To investigate the higher order dispersive effects and nonlinear effects on the solutions of HBq equation, propagation of single solitary wave, head-on collision of solitary waves and blow-up solutions are considered.

KW - Blow-up

KW - Fourier pseudo-spectral method

KW - Head-on collision of solitary waves

KW - Solitary waves

KW - The higher-order Boussinesq equation

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M3 - Article

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SN - 0165-2125

VL - 68

SP - 272

EP - 282

JO - Wave Motion

JF - Wave Motion

ER -

Higher order dispersive effects in regularized Boussinesq equation

Abstract

Bibliographical note

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Keywords

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