Instability and self-refraction of solitons

Ray tracing is used to examine the nonlinear evolution of a two-dimensional soliton with a nonplane front. The necessary stability condition for solitons in isotropic and anisotropic media is obtained. It is shown that anisotropy increases stability, while cylindrical convergence of the front leads to instability in some cases and to asymptotic stability of the soliton in others. The nonlinear stage of self-refraction of convergent and divergent regions of the soliton front is investigated. Due to nonlinear defocusing, the field in the focus of the convergent soliton remains finite, while the cylindrical front becomes plane. Then a sharp break of the front occurs followed by a singularity of the shock-soliton type which results in destruction of the soliton.