Solitary waves and vortices in a Nonlinear Schr\"odinger equation with ponderomotive nonlinearity
In the present work we revisit a ponderomotive nonlinearity model used to examine self-trapped laser beams in plasma. Upon briefly considering the exact stationary 1D solutions of the model, we extend considerations to two spatial dimensions where we find both solitonic and vortical structures. The solitary waves localized in both directions are found to be spectrally stable. However, all other structures that we consider in this model, including line solitons -- which are homogeneous 2D extensions of 1D solitons -- and vortices of topological charge S=1 and S=2 are found to be spectrally unstable. The focal point of our studies then turns to the examination of the collisions of the stable two-dimensional solitary waves for which we map a two-parameter space of soliton speeds and frequencies, in terms of the potential outcomes. While the standard scenarios of merger, inelastic collision leading to separation, separation that leaves behind a localized pulse are all possible, the intriguing outcome that we highlight here is that of a longitudinal collision yielding a transverse spliting of the solitons, either with or without a localized pulse remnant.