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Zbl 0729.35133
Grammaticos, B.; Ramani, A.; Hietarinta, J.
A search for integrable bilinear equations: The Painlevé approach. (English)
[J] J. Math. Phys. 31, No.11, 2572-2578 (1990). ISSN 0022-2488; ISSN 1089-7658/e

Summary: The possibility of the existence of new integrable partial differential equations is investigated, using the tools of singularity analysis. The equations treated are written in the Hirota bilinear formalism. It is shown here how to apply the Painlevé method directly under the bilinear form. Just by studying the dominant part of the equations, the number of cases to be considered can be limited drastically. Finally, the partial differential equations identified in a previous work of the third author [J. Math. Phys. 28, 1732-1742, 2094-2101 and 2586-2592 (1987; Zbl 0641.35073, Zbl 0658.35081 and Zbl 0658.35082); 29, No.3, 628-635 (1988; Zbl 0684.35082)] as possessing at least four soliton solutions, are shown to pass the Painlevé test as well, which is a strong indication of their integrability.

MSC 2000:: *35Q58 Other completely integrable PDE
35Q51 Solitons

Keywords: Painlevé method

Citations: Zbl 0641.35073; Zbl 0658.35081; Zbl 0658.35082; Zbl 0684.35082

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