Wronskian and Grammian solutions for (3+1)-dimensional Jimbo–Miwa equation

doi:10.1088/1674-1056/21/12/120509

Abstract In this paper, based on the Hirota's bilinear method, the Wronskian and Grammian technique, as well as several properties of determinant, a broad set of sufficient conditions consisting of systems of linear partial differential equations are presented, which guarantees that the Wronskian determinant and the Grammian determinant solve the (3+1)-dimensional Jimbo-Miwa equation in the bilinear form, and then some special exact Wronskian and Grammian solutions are obtained by solving the differential conditions. At last, with the aid of Maple, some of these special exact solutions are shown graphically.

Keywords: (3+1)-dimensional Jimbo-Miwa equation Wronskian determinant Grammian determinant exact solution

Received: 16 May 2012
Revised: 06 July 2012
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.90.+p	(Other topics in mathematical methods in physics)
	02.70.Wz	(Symbolic computation (computer algebra))

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11202161 and 11172233) and the Basic Research Fund of the Northwestern Polytechnical University, China (Grant No. GBKY1034).

Corresponding Authors: Tang Ya-Ning
E-mail: tyaning@nwpu.edu.cn

Cite this article:

Su Peng-Peng (苏朋朋), Tang Ya-Ning (唐亚宁), Chen Yan-Na (陈妍呐) Wronskian and Grammian solutions for (3+1)-dimensional Jimbo–Miwa equation 2012 Chin. Phys. B 21 120509

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Wronskian and Grammian solutions for (3+1)-dimensional Jimbo–Miwa equation

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