Construction of exact solutions to the Jimbo–Miwa equation through Bäcklund transformation and symbolic computation

Based on a simple transformation, and with the aid of symbolic computation, a Bäcklund transformation relating the Jimbo–Miwa equation and a system of linear partial differential equations is obtained, which enables us to construct exact solutions of the Jimbo–Miwa equation through the Wronskian determinants of independent solutions of the linear system. Particularly, explicit Wronskian form NN-soliton solutions for the Jimbo–Miwa equation are presented. Moreover, the introduced transformation also helps to construct bi-soliton-like solutions of the Jimbo–Miwa equation. Due to the arbitrary functions they contain, the bi-soliton-like solutions can represent various waves such as classical cross-line bi-solitons, curved bi-solitons and bi-soliton-like breathers.