Solitons, bilinear Bäcklund transformations and conservation laws for a -dimensional Bogoyavlenskii-Kadontsev-Petviashili equation in a fluid, plasma or ferromagnetic thin film

Abstract

In this paper, we investigate a $(2+1)$-dimensional Bogoyavlenskii–Kadontsev–Petviashili equation in a fluid, plasma or ferromagnetic thin film. Through the Bell polynomials, Hirota method and symbolic computation, the one- and two-kink-soliton solutions are derived. Bäcklund transformation, Lax pair and conservation laws are presented. Elastic collisions including the oblique, parallel, unidirectional and bidirectional collisions between the two-kink solitons are discussed. In addition, the relation between the velocities and wave numbers of the two-kink solitons are analysed. When wave numbers $b_j>0,{\mathit{\nu }}_{jx}$, the velocities in the x axis, increase with wave numbers $a_j$ increasing. With $b_j$ increasing, ${\mathit{\nu }}_{jx}$ increase when $a_j^4-3b_j^2>0$, while decrease when $a_j^4-3b_j^2<0$. ${\mathit{\nu }}_{jy}$, the velocities in the y axis, increase with $a_j$ increasing and $b_j$ decreasing.

Keywords:

• Fluid
• plasma or ferromagnetic thin film
• $(2+1)$-dimensional Bogoyavlenskii–Kadontsev–Petviashili equation
• Bell polynomial
• Hirota method
• conservation laws

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the National Natural Science Foundation of China [grant number 11272023]; the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), and by the Fundamental Research Funds for the Central Universities of China [grant number 2011BUPTYB02].