Novel characteristics of lump and lump–soliton interaction solutions to the generalized variable-coefficient Kadomtsev–Petviashvili equation

• Published in: Nonlinear dynamics Vol. 98; no. 1; pp. 551 - 560
• Main Authors: Xu, Hui, Ma, Zhengyi, Fei, Jinxi, Zhu, Quanyong
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2019; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Coefficients; Computational fluid dynamics; Control; Dynamical Systems; Engineering; Exponential functions; Fluid mechanics; Interaction parameters; Mechanical Engineering; Original Paper; Plasma physics; Quadratic equations; Solitary waves; Time functions; Vibration; Lump–soliton solution; Generalized variable-coefficient Kadomtsev–Petviashvili equation; Lump solution; Hirota bilinear method
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-019-05211-2

With the inhomogeneities of media taken into account, a generalized variable-coefficient Kadomtsev–Petviashvili (vcKP) equation is proposed to model nonlinear waves in fluid mechanics and plasma physics. Based on Hirota bilinear method and symbolic computation, we present lump and lump–soliton interaction solutions of the vcKP equation. These local solutions are derived by taking the auxiliary function as the positive quadratic function or the linear combination of the positive quadratic function and the exponential function. Compared with the results allowed by the constant-coefficient KP equation, lump and lump–soliton solutions for the vcKP equation possess more abundant properties. It is shown that the velocity, moving path, and maximum height of the lump are completely characterized by the time functions rather than the constant parameters. The interaction between a lump and one line soliton are still nonelastic, but the track of the lump obeys the controllable function of time. The lump interacting with resonance soliton pairs exhibits a kind of special rogue wave in which the peak emerges and evolves with the varying path. The detailed analysis and discussion of these solutions are provided and illustrated.