Grammaticos, B.; Ramani, A.; Hietarinta, J. A search for integrable bilinear equations: The Painlevé approach. (English) Zbl 0729.35133 J. Math. Phys. 31, No. 11, 2572-2578 (1990). 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. Cited in 12 Documents MSC: 35Q58 Other completely integrable PDE (MSC2000) 35Q51 Soliton equations Keywords:Painlevé method Citations:Zbl 0641.35073; Zbl 0658.35081; Zbl 0658.35082; Zbl 0684.35082 PDFBibTeX XMLCite \textit{B. Grammaticos} et al., J. Math. Phys. 31, No. 11, 2572--2578 (1990; Zbl 0729.35133) Full Text: DOI References: [1] DOI: 10.1088/0266-5611/3/2/008 · Zbl 0645.35087 [2] DOI: 10.2977/prims/1195182017 · Zbl 0557.35091 [3] DOI: 10.1063/1.528002 · Zbl 0684.35082 [4] DOI: 10.1063/1.528002 · Zbl 0684.35082 [5] DOI: 10.1063/1.524491 · Zbl 0445.35056 [6] DOI: 10.1063/1.525721 · Zbl 0514.35083 [7] DOI: 10.1016/0375-9601(82)90291-2 [8] DOI: 10.1103/PhysRevLett.53.1 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.