General breather solution to the Sasa-Satsuma (SS) equation is systematically investigated in this paper. We firstly transform the SS equation into a set of three Hirota bilinear equations under proper plane wave background. Starting from a specially arranged tau-function of the Kadomtsev-Petviashvili hierarchy and a set of eleven bilinear equations satisfied, we implement a series steps of reduction procedure, i.e., C-type reduction, dimension reduction and complex conjugate reduction, and reduce these eleven equations to three bilinear equations for the SS equation. Meanwhile, general breather solution to the SS equation is found in determinant of even order. The one- and two-breather solutions are calculated and analyzed in details.
Wu Chengfa, Wei Bo, Shi Changyan and Feng Bao-Feng 2022Multi-breather solutions to the Sasa–Satsuma equation. Proc. R. Soc. A. 4782021071120210711 http://doi.org/10.1098/rspa.2021.0711
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Proceedings of the Royal Society A