Abstract
The Sasa-Satsuma equation is considered. The Painlevé test for partial differential equations with application of the Kruskal variable is used to investigate the necessary condition of integrability of the equation. It is shown that the equation does not pass the Painlevé test in the general case. However, there exist constraints on parameters of the equation, when all Fuchs indices are integers. In these cases the Laurent series expansions of the solution exit and, consequently, there exist analytical solutions of this partial differential equation. We confirm that there are two integrable cases, at which the Sasa–Satsuma equation passes the Painlevé test. We also obtain that there is another set of parameter values at which the equation can be an integrable.
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