0000000000396824
AUTHOR
Mariana Haragus
Transverse instability of periodic and generalized solitary waves for a fifth-order KP model
We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.
Numerical study of the stability of the Peregrine solution
International audience; The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.