An asymptotic approach to solitary wave instability and critical collapse in long-wave KdV-type evolution equations

Instability development and critical collapse of solitary waves are considered in the framework of generalized Korteweg-de Vries (KdV) equations in one and two dimensions. An analytical theory of the solitary wave dynamics and generation of radiation is constructed for the critical case when the solitary waves are weakly unstable. Characteristic types of the global, essentially nonlinear evolution of the unstable solitary waves are analyzed for …