Solitons to rogue waves transition, lump solutions and interaction solutions for the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid dynamics

ABSTRACT

In this work, we investigate the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation in fluid dynamics, which plays an important role in depicting weakly dispersive waves propagated in a quasi-media and fluid mechanics. By employing Hirota's bilinear method, we derive the one- and two-soliton solutions of the equation. Moreover, we reduce those soliton solutions to the periodic line waves and exact breather waves by considering different parameters. A long wave limit is used to derive the rogue wave solutions. Based on the resulting bilinear representation, we introduce two types of special polynomial functions, which are employed to find the lump solutions and interaction solutions between lump and stripe soliton. It is hoped that our results can be used to enrich dynamic behaviours of the (3+1)-dimensional BKP-type equations.

KEYWORDS:

• The generalized B-type Kadomtsev–Petviashvili equation
• breather wave solutions
• rogue wave solutions
• lump solitons
• interaction solutions

2010 AMS MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35Q51
• 35Q53
• 74J30

Acknowledgments

We express our sincere thanks to the Editor and the Referees for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Jiangsu Province Natural Science Foundation of China [Grant No. BK20181351], the Postgraduate Research & Practice Program of Education & Teaching Reform of CUMT [Grant No. YJSJG_2018_036], the ‘Qinglan Engineering project’ of Jiangsu Universities, the National Natural Science Foundation of China [Grant No. 11301527], the Fundamental Research Fund for the Central Universities [Grant No. 2017XKQY101], and the General Financial Grant from the China Postdoctoral Science Foundation [Grant Nos 2015M570498 and 2017T100413].