Fractal and chaotic patterns of Nizhnik-Novikov-Veselov system derived from a periodic wave solution

Starting from an extended mapping method and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for (2+1)-dimensional Nizhnik-Novikov-Veselov system (NNV) are derived. Usually, in terms of solitary wave solutions and rational function solutions, one can find some important localized excitations. However, based on the derived periodic wave solution in this Letter, we find that some novel and interesting localized coherent excitations such as stochastic fractal patterns, regular fractal patterns, chaotic line soliton patterns and chaotic patterns also exist in the NNV system as considering appropriate boundary conditions and/or initial qualifications.