Multi-breather solutions to the Sasa-Satsuma equation

TL;DR

This paper systematically derives general breather solutions for the Sasa-Satsuma equation using Hirota bilinear forms and reduction techniques, providing explicit one- and two-breather solutions with detailed analysis.

Contribution

It introduces a novel method to obtain general breather solutions of the SS equation via tau-functions and reduction procedures, expanding the understanding of its solution space.

Findings

Derived general breather solutions in determinant form

Explicit one- and two-breather solutions calculated

Detailed analysis of breather dynamics and properties

Abstract

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.