Instantaneous solitons and fractal solitons for a (2+1)-dimensional nonlinear system

By an improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the (2+1)-dimensional Broek–Kaup system is derived. Based on the derived solitary wave solution and by selecting appropriate functions, some novel localized excitations such as instantaneous solitons and fractal solitons are investigated.