On the full dispersion Kadomtsev–Petviashvili equations for dispersive elastic waves

Name: On the full dispersion Kadomtsev–Petviashvili equations for dispersive elastic waves
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	On the full dispersion Kadomtsev–Petviashvili equations for dispersive elastic waves
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2022-09
Basım Yeri	- Elsevier
Konu	Full dispersion, Kadomtsev–Petviashvili equation, Nonlocal elasticity, Solitary waves, Transverse instability
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0165-2125
Kayıt Numarası	cd4a5e00-d710-430c-850a-1bb63e8210db
Lokasyon	Natural and Mathematical Sciences
Tarih	2022-09
Örnek Metin	Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev–Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies analogous full dispersive KP models of nonlinear elastic waves propagating in a nonlocal elastic medium. In particular we consider anti-plane shear elastic waves which are assumed to be small-amplitude long waves. We propose two different full dispersive extensions of the KP equation in the case of cubic nonlinearity and ”negative dispersion”. One of them is called the Whitham-type full dispersion KP equation and the other one is called the BBM-type full dispersion KP equation. Most of the existing KP-type equations in the literature are particular cases of our full dispersion KP equations. We also introduce the simplified models of the new proposed full dispersion KP equations by approximating the operators in the equations. We show that the line solitary wave solution of a simplified form of the Whitham-type full dispersion KP equation is linearly unstable to long-wavelength transverse disturbances if the propagation speed of the line solitary wave is greater than a certain value. A similar analysis for a simplified form of the BBM-type full dispersion KP equation does not provide a linear instability assessment.
DOI	10.1016/j.wavemoti.2022.103015
Cilt	114

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On the full dispersion Kadomtsev–Petviashvili equations for dispersive elastic waves

Yazar Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

Basım Tarihi 2022-09

Basım Yeri - Elsevier

Konu Full dispersion, Kadomtsev–Petviashvili equation, Nonlocal elasticity, Solitary waves, Transverse instability

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0165-2125

Kayıt Numarası cd4a5e00-d710-430c-850a-1bb63e8210db

Lokasyon Natural and Mathematical Sciences

Tarih 2022-09

Örnek Metin Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev–Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies analogous full dispersive KP models of nonlinear elastic waves propagating in a nonlocal elastic medium. In particular we consider anti-plane shear elastic waves which are assumed to be small-amplitude long waves. We propose two different full dispersive extensions of the KP equation in the case of cubic nonlinearity and ”negative dispersion”. One of them is called the Whitham-type full dispersion KP equation and the other one is called the BBM-type full dispersion KP equation. Most of the existing KP-type equations in the literature are particular cases of our full dispersion KP equations. We also introduce the simplified models of the new proposed full dispersion KP equations by approximating the operators in the equations. We show that the line solitary wave solution of a simplified form of the Whitham-type full dispersion KP equation is linearly unstable to long-wavelength transverse disturbances if the propagation speed of the line solitary wave is greater than a certain value. A similar analysis for a simplified form of the BBM-type full dispersion KP equation does not provide a linear instability assessment.

DOI 10.1016/j.wavemoti.2022.103015

Cilt 114