Novel evolutionary behaviors of N-soliton solutions for the (3+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petciashvili equation - Li, Longxing; Cheng, Bitao; Dai, Zhengde (Nonlinear dynamics, 2024)
Under investigation in this work is to explore novel evolutionary behaviors of N -soliton solutions for the (3+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petciashvili (gCH-KP) equation, which is proposed to describe the role of dispersion in the formation of patterns in liquid drops. Resonant soliton solutions composed of soliton molecules and Y -type soliton solutions are constructed by introducing appropriate condition to N -soliton solutions. High-order breather solutions are generated with the complex conjugate relation of the parameters of N -soliton solutions, and rational breather solution is obtained by breather limit method. Moreover, a variety of hybrid solutions are derived by combining with resonant condition, long-wave limit approach and parameter complexification method, which contain soliton molecule, Y -type soliton, high-order breathers, lump soliton and their interaction diagrams are simulated explicitly. These received results greatly enrich the solutions and nonlinear dynamical behaviors of gCH-KP equation, and it could be helpful for understanding in nonlinear partial differential equation deeply.