Modulated periodic wavetrains in the spherical Gardner equation

Gunay Aslanova; Ali Demirci; Semra Ahmetolan

doi:10.1016/j.wavemoti.2021.102844

Modulated periodic wavetrains in the spherical Gardner equation

Gunay Aslanova^*, Ali Demirci, Semra Ahmetolan

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Technical University

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

6 Citations (Scopus)

Abstract

The spherical Gardner (sG) equation is derived by reducing the (3+1)-dimensional Gardner–Kadomtsev–Petviashvili (Gardner–KP) equation with a similarity reduction. As a special case, the step-like initial condition is considered along a paraboloid front. By applying a multiple-scale expansion, a system of first order partial differential equations for the slowly varying parameters of a periodic wavetrain is obtained. The corresponding modulation system is transformed into a simpler form with the help of Riemann type variables. This basic form is important to investigate the dispersive shock wave (DSW) phenomena in the sG equation. DSW solution is also compared with the numerical solution of the sG equation and good agreement is found between these solutions.

Original language	English
Article number	102844
Journal	Wave Motion
Volume	109
DOIs	https://doi.org/10.1016/j.wavemoti.2021.102844
Publication status	Published - Feb 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.

Funding

We thank D.E. Baldwin for the MATLAB codes of the ETDRK4 method used in this study. Also, we would like to thank the anonymous referees for carefully reading the manuscript and acknowledge their constructive recommendations on the presentation of the paper.

Keywords

Dispersive shock waves
Gardner–KP equation
Whitham modulation theory

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10.1016/j.wavemoti.2021.102844

Cite this

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title = "Modulated periodic wavetrains in the spherical Gardner equation",

abstract = "The spherical Gardner (sG) equation is derived by reducing the (3+1)-dimensional Gardner–Kadomtsev–Petviashvili (Gardner–KP) equation with a similarity reduction. As a special case, the step-like initial condition is considered along a paraboloid front. By applying a multiple-scale expansion, a system of first order partial differential equations for the slowly varying parameters of a periodic wavetrain is obtained. The corresponding modulation system is transformed into a simpler form with the help of Riemann type variables. This basic form is important to investigate the dispersive shock wave (DSW) phenomena in the sG equation. DSW solution is also compared with the numerical solution of the sG equation and good agreement is found between these solutions.",

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author = "Gunay Aslanova and Ali Demirci and Semra Ahmetolan",

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AU - Demirci, Ali

AU - Ahmetolan, Semra

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N2 - The spherical Gardner (sG) equation is derived by reducing the (3+1)-dimensional Gardner–Kadomtsev–Petviashvili (Gardner–KP) equation with a similarity reduction. As a special case, the step-like initial condition is considered along a paraboloid front. By applying a multiple-scale expansion, a system of first order partial differential equations for the slowly varying parameters of a periodic wavetrain is obtained. The corresponding modulation system is transformed into a simpler form with the help of Riemann type variables. This basic form is important to investigate the dispersive shock wave (DSW) phenomena in the sG equation. DSW solution is also compared with the numerical solution of the sG equation and good agreement is found between these solutions.

AB - The spherical Gardner (sG) equation is derived by reducing the (3+1)-dimensional Gardner–Kadomtsev–Petviashvili (Gardner–KP) equation with a similarity reduction. As a special case, the step-like initial condition is considered along a paraboloid front. By applying a multiple-scale expansion, a system of first order partial differential equations for the slowly varying parameters of a periodic wavetrain is obtained. The corresponding modulation system is transformed into a simpler form with the help of Riemann type variables. This basic form is important to investigate the dispersive shock wave (DSW) phenomena in the sG equation. DSW solution is also compared with the numerical solution of the sG equation and good agreement is found between these solutions.

KW - Dispersive shock waves

KW - Gardner–KP equation

KW - Whitham modulation theory

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DO - 10.1016/j.wavemoti.2021.102844

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VL - 109

JO - Wave Motion

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ER -

Modulated periodic wavetrains in the spherical Gardner equation

Abstract

Bibliographical note

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Keywords

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