Degeneration of N-soliton solutions for a (3+1)-dimensional nonlinear model in shallow water waves - Li, Longxing; Dai, Zhengde; Cheng, Bitao (Nonlinear dynamics, 2023)
With the support of bilinear method, specific N -soliton solutions of a ( 3 + 1 )-dimensional nonlinear model are proposed, and various solutions are constructed through the different degeneration processes of N -soliton solutions. On the basis of defining a novel constraint condition on N -soliton solutions, resonance Y -type solitons are found out. Under complex conjugating method (complexification method), N -soliton solutions could convert to high-order breathers ( T -order breathers). Resorting to long wave limit technique, high-order lumps ( M -order lumps) are obtained. During the partial degeneration of N -soliton solutions, combining complexification method and long wave limit technique, abundant interaction solutions composed of soliton, breather and lump are yielded. The corresponding numerical simulations are presented to demonstrate the dynamic behaviors of the obtained solutions.