Existence and stability of traveling waves for a class of nonlocal nonlinear equations

Name: Existence and stability of traveling waves for a class of nonlocal nonlinear equations
Author: Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

İsim	Existence and stability of traveling waves for a class of nonlocal nonlinear equations
Yazar	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Basım Tarihi:	2015-05-01
Basım Yeri	- Elsevier
Konu	Solitary waves, Orbital stability, Boussinesq equation, Double dispersion equation, Concentration-compactness, Klein–Gordon equation
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	0022-247X
Kayıt Numarası	ff6dd394-4c58-4c2a-8fd5-c7c8d51efa89
Lokasyon	Natural and Mathematical Sciences
Tarih	2015-05-01
Notlar	TÜBİTAK
Örnek Metin	In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: utt−Luxx=B(±\|u\|p−1u)xx, p>1. The main characteristic of this class of equations is the existence of two sources of dispersion, characterized by two coercive pseudo-differential operators L and B . Members of the class arise as mathematical models for the propagation of dispersive waves in a wide variety of situations. For instance, all Boussinesq-type equations and the so-called double-dispersion equation are members of the class. We first establish the existence of traveling wave solutions to the nonlocal wave equations considered. We then obtain results on the orbital stability or instability of traveling waves. For the case L=I, corresponding to a class of Klein–Gordon-type equations, we give an almost complete characterization of the values of the wave velocity for which the traveling waves are orbitally stable or unstable by blow-up.
DOI	10.1016/j.jmaa.2014.12.039
Cilt	425

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Kaynağa git

Existence and stability of traveling waves for a class of nonlocal nonlinear equations

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

Basım Tarihi 2015-05-01

Basım Yeri - Elsevier

Konu Solitary waves, Orbital stability, Boussinesq equation, Double dispersion equation, Concentration-compactness, Klein–Gordon equation

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 0022-247X

Kayıt Numarası ff6dd394-4c58-4c2a-8fd5-c7c8d51efa89

Lokasyon Natural and Mathematical Sciences

Tarih 2015-05-01

Notlar TÜBİTAK

Örnek Metin In this article we are concerned with the existence and orbital stability of traveling wave solutions of a general class of nonlocal wave equations: utt−Luxx=B(±|u|p−1u)xx, p>1. The main characteristic of this class of equations is the existence of two sources of dispersion, characterized by two coercive pseudo-differential operators L and B . Members of the class arise as mathematical models for the propagation of dispersive waves in a wide variety of situations. For instance, all Boussinesq-type equations and the so-called double-dispersion equation are members of the class. We first establish the existence of traveling wave solutions to the nonlocal wave equations considered. We then obtain results on the orbital stability or instability of traveling waves. For the case L=I, corresponding to a class of Klein–Gordon-type equations, we give an almost complete characterization of the values of the wave velocity for which the traveling waves are orbitally stable or unstable by blow-up.

DOI 10.1016/j.jmaa.2014.12.039

Cilt 425