| Title | On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type |
| Authors | Mats Ehrnstrom, Mark D. Groves, Erik Wahlén |
| Alternative Location | http://dx.doi.org/10.1088/0..., Restricted Access |
| Publication | Nonlinearity |
| Year | 2012 |
| Volume | 25 |
| Issue | 10 |
| Pages | 2903 - 2936 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | IOP Publishing |
| Abstract 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. |
| ISBN/ISSN/Other | ISSN: 0951-7715 |
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