Instability of solitary wave solutions to long-wavelength transverse perturbationsin the generalized Kadomtsev-Petviashvili equation with negative dispersion.
The present paper is a more detailed article of the previously published Letter [Phys. Rev. Lett. 84, 3065 (2000)]], which discovered the transversely unstable solitary wave solutions of the generalized Kadomtsev-Petviashvili (GKP) equation with negative dispersion. In addition to detailed explanation of stability analysis to long-wavelength transverse perturbations, numerical calculation of the GKP equation is carried out here to study the transverse stability to perturbations of finite wavelength. The numerical results show that there is a short-wavelength cutoff to the transverse instability. Moreover, we reveal the existence of transversely unstable solitons.
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan.
Takeshi
T
Kataoka
Michihisa
M
Tsutahara