Instability and decay of solitary waves in the Davey-Stewartson 1 system

The exact solutions to the Davey-Stewartson 1 equations are constructed to describe the development of a transversal solitary wave instability. Two types of plane dark soliton decays into two-dimensional solitary waves are found and analysed. It is also shown that the transversal instability of one-dimensional waveguides leads only to a shift of their drift velocity under the action of nonlocalized, inhomogeneous perturbations.