Wronskian and Grammian solutions for a [formula omitted]-dimensional Date–Jimbo–Kashiwara–Miwa equation

Abstract

In this paper, a (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation is investigated. Based on the Hirota method and auxiliary variable, Bäcklund transformation is obtained. Under certain conditions, the Hirota bilinear forms can be reduced to the Plücker and Jacobi identities via the Wronskian and Grammian solutions. Through the Wronskian technique and Pfaffian derivative formulae, N-soliton solutions in the Wronskian and Grammian are given. Graphically presented, soliton collisions are elastic both in the Wronskian and Grammian, and after each collision, the solitons keep their amplitudes unchanged except for the phase shifts.