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

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Abstract

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 N-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. © 2012 Elsevier B.V. All rights reserved.

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Lü, Z., Su, J., & Xie, F. (2013). Construction of exact solutions to the Jimbo-Miwa equation through Bäcklund transformation and symbolic computation. Computers and Mathematics with Applications, 65(4), 648–656. https://doi.org/10.1016/j.camwa.2012.11.009

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