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

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Istanbul Technical University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

6 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Makale numarası	102844
Dergi	Wave Motion
Hacim	109
DOI'lar	https://doi.org/10.1016/j.wavemoti.2021.102844
Yayın durumu	Yayınlandı - Şub 2022

Bibliyografik not

Publisher Copyright:
© 2021 Elsevier B.V.

Finansman

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.

Belgeye Erişim

10.1016/j.wavemoti.2021.102844

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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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.",

keywords = "Dispersive shock waves, Gardner–KP equation, Whitham modulation theory",

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

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2022",

month = feb,

doi = "10.1016/j.wavemoti.2021.102844",

language = "English",

volume = "109",

journal = "Wave Motion",

issn = "0165-2125",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Modulated periodic wavetrains in the spherical Gardner equation

AU - Aslanova, Gunay

AU - Demirci, Ali

AU - Ahmetolan, Semra

PY - 2022/2

Y1 - 2022/2

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

UR - https://www.scopus.com/pages/publications/85120824701

U2 - 10.1016/j.wavemoti.2021.102844

DO - 10.1016/j.wavemoti.2021.102844

M3 - Article

AN - SCOPUS:85120824701

SN - 0165-2125

VL - 109

JO - Wave Motion

JF - Wave Motion

M1 - 102844

ER -

Modulated periodic wavetrains in the spherical Gardner equation

Özet

Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap