Auto-Bäcklund transformations and soliton solutions on the nonzero background for a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid

• Published in: Nonlinear dynamics Vol. 111; no. 9; pp. 8647 - 8658
• Main Authors: Zhou, Tian-Yu, Tian, Bo, Shen, Yuan, Gao, Xiao-Tian
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2023; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Control; Dynamical Systems; Engineering; Fluid mechanics; Lie groups; Mechanical Engineering; Original Paper; Solitary waves; Transformations; Vibration; Interactions; (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation; Fluid; Auto-Bäcklund transformations; Solitons
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-08260-w

In this paper, a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid is investigated. By the virtue of the truncated Painlevé expansion, a set of the auto-Bäcklund transformations of that equation is worked out. Based on the auto-Bäcklund transformations with certain non-trivial seed solutions, one-, two-, three- and N -soliton solutions on the nonzero background of that equation are derived with N as a positive integer. According to those two-soliton solutions, X - and inelastic-type soliton solutions are obtained. Via the asymptotic analysis, influence of the coefficients for the above equation is discussed and the interactions between the solitons are also studied. Then, those solitons and interactions are shown graphically.