Novel evolutionary behaviors of N-soliton solutions for the (3+1)-dimensional generalized Camassa–Holm–Kadomtsev–Petciashvili equation

• Published in: Nonlinear dynamics Vol. 112; no. 3; pp. 2157 - 2173
• Main Authors: Li, Longxing, Cheng, Bitao, Dai, Zhengde
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.02.2024; Springer Nature B.V
• Subjects: Automotive Engineering; Breathers; Classical Mechanics; Control; Drops (liquids); Dynamical Systems; Engineering; Investigations; Mathematics; Mechanical Engineering; Nonlinear differential equations; Original Paper; Parameters; Partial differential equations; Solitary waves; Vibration; Camassa–Holm–Kadomtsev–Petciashvili equation; Breather solution; Resonant soliton; Hybrid solution; soliton solution
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-09122-1

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.