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On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type

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Author

Summary, in English

We consider a class of pseudodifferential evolution equations of the form u(t) + (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.

Department/s

Publishing year

2012

Language

English

Pages

2903-2936

Publication/Series

Nonlinearity

Volume

25

Issue

10

Document type

Journal article

Publisher

London Mathematical Society / IOP Science

Topic

  • Mathematics

Status

Published

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 0951-7715