Dynamics of kink solitary waves and lump waves with interaction phenomena in a generalized (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation

Abstract

By using symbolic computation methods, we systematically study a generalized (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq (KP-Boussinesq) equation, which can be used to explain some interesting physical phenomena in the fields of fluids. We first obtain bilinear representation of the equation by employing the properties of Bell's polynomials. Based on that, its a series of exact solutions, such as one kink soliton solutions, two kink soliton solutions and lump wave solutions, are constructed in detail. It is worth mentioning that we also study the interaction solutions between lump waves and kink waves. Moreover, in order to describe the dynamic behaviours of those solutions, some graphical analyses are given by selecting different parameter values in such solutions. Those analyses are helpful for enriching the physical phenomena in KP-type equations.

Keywords:

• A generalized (3+1)-dimensional KP-Boussinesq equation
• Bell's polynomial
• lump waves
• kink solitary waves
• interaction phenomena

2010 Mathematics Subject Classifications:

• 35Q51
• 35Q53
• 35C08

Acknowledgments

The authors would like to thank the editor and the referees for their valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Fundamental Research Fund for the Central Universities [grant number 2019ZDPY07].