Abstract We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Jimbo－Miwa (JM) equation as an example. Using the extended homogeneous balance method, one can find a B?cklund transformation to decompose the (3+1)-dimensional JM equation into a linear partial differential equation and two bilinear partial differential equations. Starting from these linear and bilinear partial differential equations, some multiple soliton solutions for the (3+1)-dimensional JM equation are obtained by introducing a class of formal solutions.
Received: 13 September 2001
Revised: 20 December 2001
Accepted manuscript online:
PACS:
02.30.Jr
(Partial differential equations)
Fund: Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No 100039).
Cite this article:
Zhang Jie-Fang (张解放), Wu Feng-Min (吴锋民) Bäcklund transformation and multiple soliton solutions for the (3+1)-dimensional Jimbo-Miwa equation 2002 Chinese Physics 11 425
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