Multi-breather solutions to the Sasa–Satsuma equation

Abstract

General breather solution to the Sasa–Satsuma equation (SSE) is systematically investigated in this paper. We firstly transform the SSE into a set of three Hirota bilinear equations under a proper plane wave boundary condition. Starting from a specially arranged tau-function of the Kadomtsev–Petviashvili hierarchy and a set of 11 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 11 equations to three bilinear equations for the SSE. Meanwhile, the general breather solution to the SSE is found in determinant of even order. The one- and two-breather solutions are calculated and analysed in detail.