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On the transverse stability of smooth solitary waves in a two-dimensional Camassa–Holm equation.
- Source :
-
Journal de Mathematiques Pures et Appliquees . Aug2024, Vol. 188, p1-25. 25p. - Publication Year :
- 2024
-
Abstract
- We consider the propagation of smooth solitary waves in a two-dimensional generalization of the Camassa–Holm equation. We show that transverse perturbations to one-dimensional solitary waves behave similarly to the KP-II theory. This conclusion follows from our two main results: (i) the double eigenvalue of the linearized equations related to the translational symmetry breaks under a transverse perturbation into a pair of the asymptotically stable resonances and (ii) small-amplitude solitary waves are linearly stable with respect to transverse perturbations. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EIGENVALUE equations
*EQUATIONS
*SYMMETRY breaking
Subjects
Details
- Language :
- English
- ISSN :
- 00217824
- Volume :
- 188
- Database :
- Academic Search Index
- Journal :
- Journal de Mathematiques Pures et Appliquees
- Publication Type :
- Academic Journal
- Accession number :
- 178464702
- Full Text :
- https://doi.org/10.1016/j.matpur.2024.05.008