Abstract
Using a cubic-quintic nonlinear Schrödinger equation as a model, we study the existence and interactions of two-dimensional (2D) solitons on top of a continuous-wave background. It is shown that the 2D solitons exist in the form of dark or antidark lumps, which are described by an effective KP (Kadomtsev-Petviashvili)-I equation. Interactions and collisions of 2D solitons are investigated using both analytical and numerical techniques. The most remarkable feature of the interaction is formation of a transient long-lived quasi-bound state of two colliding solitons, before they separate.
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