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

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

中国物理B ›› 2012, Vol. 21 ›› Issue (12): 120509-120509.doi: 10.1088/1674-1056/21/12/120509

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

苏朋朋, 唐亚宁, 陈妍呐

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

收稿日期:2012-05-16 修回日期:2012-07-06 出版日期:2012-11-01 发布日期:2012-11-01
基金资助:
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).

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

Su Peng-Peng (苏朋朋), Tang Ya-Ning (唐亚宁), Chen Yan-Na (陈妍呐)

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

Received:2012-05-16 Revised:2012-07-06 Online:2012-11-01 Published:2012-11-01
Contact: Tang Ya-Ning E-mail:tyaning@nwpu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

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

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.

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

中图分类号: (Solitons)

05.45.Yv

02.90.+p (Other topics in mathematical methods in physics) 02.70.Wz (Symbolic computation (computer algebra))

苏朋朋, 唐亚宁, 陈妍呐. Wronskian and Grammian solutions for (3+1)-dimensional Jimbo–Miwa equation[J]. 中国物理B, 2012, 21(12): 120509-120509.

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[J]. Chin. Phys. B, 2012, 21(12): 120509-120509.

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

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

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