Some remarks on the stability and instability properties of solitary waves for the double dispersion equation

Name: Some remarks on the stability and instability properties of solitary waves for the double dispersion equation
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	Some remarks on the stability and instability properties of solitary waves for the double dispersion equation
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2015
Basım Yeri	- Estonian Academy of Sciences
Konu	Double dispersion equation, Boussinesq equation, Solitary waves, Instability by blow-up, Orbital stability, Travelling waves
Tür	Belge
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	2-s2.0-84939511087
Kayıt Numarası	5ed74ebd-50fb-4c12-8453-3ba3408baf81
Lokasyon	Natural and Mathematical Sciences
Tarih	2015
Örnek Metin	In this article we give a review of our recent results on the instability and stability properties of travelling wave solutions of the double dispersion equation utt − uxx + auxxxx − buxxtt = −(\|u\|p−1u)xx for p > 1, a ≥ b > 0. After a brief reminder of the general class of nonlocal wave equations to which the double dispersion equation belongs, we summarize our findings for both the existence and orbital stability/instability of travelling wave solutions to the general class of nonlocal wave equations. We then state (i) the conditions under which travelling wave solutions of the double dispersion equation are unstable by blow-up and (ii) the conditions under which the travelling waves are orbitally stable. We plot the instability/stability regions in the plane defined by wave velocity and the quotient b/a for various values of p.
DOI	10.3176/proc.2015.3.09
Cilt	64

Kaynağa git Özyeğin Üniversitesi

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Özyeğin Üniversitesi

Kaynağa git

Some remarks on the stability and instability properties of solitary waves for the double dispersion equation

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

Basım Tarihi 2015

Basım Yeri - Estonian Academy of Sciences

Konu Double dispersion equation, Boussinesq equation, Solitary waves, Instability by blow-up, Orbital stability, Travelling waves

Tür Belge

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 2-s2.0-84939511087

Kayıt Numarası 5ed74ebd-50fb-4c12-8453-3ba3408baf81

Lokasyon Natural and Mathematical Sciences

Tarih 2015

Örnek Metin In this article we give a review of our recent results on the instability and stability properties of travelling wave solutions of the double dispersion equation utt − uxx + auxxxx − buxxtt = −(|u|p−1u)xx for p > 1, a ≥ b > 0. After a brief reminder of the general class of nonlocal wave equations to which the double dispersion equation belongs, we summarize our findings for both the existence and orbital stability/instability of travelling wave solutions to the general class of nonlocal wave equations. We then state (i) the conditions under which travelling wave solutions of the double dispersion equation are unstable by blow-up and (ii) the conditions under which the travelling waves are orbitally stable. We plot the instability/stability regions in the plane defined by wave velocity and the quotient b/a for various values of p.

DOI 10.3176/proc.2015.3.09

Cilt 64