Evolution and emergence of new lump and interaction solutions to the (2+1)- dimensional Nizhnik-Novikov-Veselov system

Exploiting Hirota's bilinear method, we investigate N-soliton solutions, N-order rational solutions, and M-order lump solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov system. Based on this foundation, different forms of breather wave solutions and lump solutions are obtained by using the parameter limit method. Besides, by constructing a new test function, we study the interaction between lump solutions and soliton solutions of different types, such as the rational-cosh type, rational-cosh-cos type, and rational-cos type. Meanwhile, we also provide a large number of images of the evolution of the spatial structure by selecting different parameter values in order to better show the asymptotic behavior of the exact solution obtained in this paper.