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

Abstract

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.

Degeneration of N-solitons and interaction of higher-order solitons for the (2+1)-dimensional generalized Hirota-Satsuma-Itoequation

“…At these two points Ω 1,2 , lump solution (16) respectively reaches maximum value Q which show a valley and a peak in spatial structure (see figure5(a)), and presents algebraically decays in all aspects of space. The lump solution with this structure characteristics is also called the bright-dark lump solution[27][28][29].Similar to the calculation of N = 2, when N = 4, M = 2, taking = = -, we can get 2-order lump solution (see figure 5(b)). When N = 6, M = 3, taking = in (13), we can get 3-order lump solution (see figure 5(c)).…”