Transverse stability of solitary travelling waves in a two-dimensional Camassa-Holm equation
A talk in the Oberseminar Analysis series by
Anna Geyer from TU Delft
| Abstract: | The Camassa-Holm equation models the unidirectional propagation of waves in shallow water. The stability of its solitary traveling wave solutions with respect to localised perturbations has been extensively studied. In this talk, I will focus on transverse stability, that is, stability with respect to perturbations transverse to the direction of propagation. To this end we consider a two-dimensional generalisation of the Camassa-Holm equation and study the spectrum of an operator which arises after linearisation around the perturbation in suitably weighted spaces. We show that (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.
The talk is based on joint work with Yue Liu and Dmitry Pelinovsky. Zoom Meeting ID: 684 0498 9843 Passcode: 241051 $\href{https://uni-bielefeld.zoom-x.de/j/68404989843?pwd=cWNqT3FFZWFxMW1RQ3FvUkZ0MG9Jdz09}{\textbf{Join Zoom Meeting}}$ |