Darboux transformation and soliton solutions of the generalized Sasa-Satsuma equation

TL;DR

This paper constructs Darboux transformations for the generalized Sasa-Satsuma equation, deriving various soliton solutions and analyzing their properties, contributing to the understanding of higher-order nonlinear Schrödinger equations in optical fiber contexts.

Contribution

It introduces a Darboux transformation framework for the generalized Sasa-Satsuma equation and derives new soliton solutions with their dynamics and conservation laws.

Findings

Derived hump-type, breather-type, and periodic soliton solutions.

Analyzed the asymptotic behavior of solitons.

Established infinite conservation laws for the equation.

Abstract

The Sasa-Satsuma equation, a higher-order nonlinear Schr\"{o}dinger equation, is an important integrable equation, which displays the propagation of femtosecond pulses in optical fibers. In this paper, we investigate a generalized Sasa-Satsuma(gSS) equation. The Darboux transformation(DT) for the focusing and defocusing gSS equation is constructed. By using the DT, various of soliton solutions for the generalized Sasa-Satsuma equation are derived, including hump-type, breather-type and periodic soliton. Dynamics properties and asymptotic behavior of these soliton solutions are analyzed. Infinite number conservation laws and conserved quantities for the gSS equation are obtained.