Result: On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
Title:
On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
Authors:
Source:
Nonlinearity (Bristol. Print). 25(10):2903-2936
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 22 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Théorie des opérateurs, Operator theory, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Approximation non linéaire, Non linear approximation, Aproximación no lineal, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Equation pseudodifférentielle, Pseudodifferential equation, Ecuación seudodiferencial, Equation évolution, Evolution equation, Ecuación evolución, Fonctionnelle, Functional, Funciónal, Lissage, Smoothing, Alisamiento, Minimisation, Minimization, Minimización, Méthode lissage, Smoothing methods, Onde solitaire, Solitary wave, Onda solitaria, Opérateur linéaire, Linear operator, Operador lineal, Physique mathématique, Mathematical physics, Física matemática, Principe compacité concentration, Concentration compactness principle, Principio compacidad concentración, 35XX, 47Axx, 58D25, 65F35, 65J08, 65M99, 65Mxx, 65N99, 65Nxx, Stabilité solution
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Institut für Angewandte Mathematik, Leibniz Universitat Hannover, Welfengarten 1, 30167 Hannover, Germany
Fachrichtung 6,1-Mathematik, Universitat des Saarlandes, Postfach 151 150, 66041 Saarbrücken, Germany
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, United Kingdom
Centre for Mathematical Sciences, Lund University, PO Box 118, 221 00 Lund, Sweden
Institut für Angewandte Mathematik, Leibniz Universitat Hannover, Welfengarten 1, 30167 Hannover, Germany
Fachrichtung 6,1-Mathematik, Universitat des Saarlandes, Postfach 151 150, 66041 Saarbrücken, Germany
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, United Kingdom
Centre for Mathematical Sciences, Lund University, PO Box 118, 221 00 Lund, Sweden
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26437275
Database:
PASCAL Archive
Further Information
We consider a class of pseudodifferential evolution equations of the form ut + (n(u) + Lu)x = 0, in which L is a linear smoothing operator and n is at least quadratic near the origin; this class includes in particular the Whitham equation. A family of solitary-wave solutions is found using a constrained minimization principle and concentration-compactness methods for noncoercive functionals. The solitary waves are approximated by (scalings of) the corresponding solutions to partial differential equations arising as weakly nonlinear approximations; in the case of the Whitham equation the approximation is the Korteweg-deVries equation. We also demonstrate that the family of solitary-wave solutions is conditionally energetically stable.