Eur. Phys. J. Plus (2021) 136: 1097
https://doi.org/10.1140/epjp/s13360-021-02065-9

Regular Article

Variety interaction solutions comprising lump solitons for a generalized BK equation by trilinear analysis

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

^a j_manafianheris@tabrizu.ac.ir

Received: 29 March 2021
Accepted: 11 June 2021
Published online: 31 October 2021

Abstract

In this paper, we study a new generalized (2+1)-dimensional Bogoyavlensky–Konopelchenko equation which is considered in soliton theory and generated by considering the Hirota trilinear operators. We retrieve some novel exact analytical solutions, including lump-type wave, breather wave as well as breather-kink-type wave, and lump-kink wave solutions for a (2+1)-dimensional -gBK equation by Maple symbolic computations. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota trilinear forms and their generalized equivalences. Through the way of resetting different space constants, we adjust the coordinates of kink-type waves in order for them colliding with the breather wave; after that, the transformed kink-type waves gradually swallow the breather wave. Also, the N-soliton wave solutions for the (2+1)-dimensional gBK equation are successfully constructed through using a perturbation method. Lastly, the graphical simulations of the exact solutions are depicted.