New types of interactions between solitary waves in (2 + 1)-dimensions

By applying a special Bäcklund transformation, a general variable separation solution of the (2 + 1)-dimensional nonlinear Schrödinger equation is derived. Based on the quite universal variable separation solution and by selecting appropriate functions, a new types of interaction structure between the multi-valued and the single-valued solitary waves, such as fractal semifolded localized structure is investigated in detail and find the interactions possess some novel and interesting features.