Soliton solutions to the coupled Sasa-Satsuma equation under mixed boundary conditions

TL;DR

This paper derives and analyzes bright-dark soliton solutions for the coupled Sasa-Satsuma equation using the KP reduction method, contributing new explicit solutions and insights into their dynamics.

Contribution

It introduces a novel approach to obtain explicit bright-dark soliton solutions for the CSS equation via KP reduction from the four-component Hirota equation.

Findings

Explicit bright-dark soliton solutions are constructed.

Dynamical behaviors of solitons are thoroughly analyzed.

Solutions reveal rich interaction properties.

Abstract

In this paper, we derive general bright-dark soliton solutions to the coupled Sasa-Satsuma (CSS) equation using the Kadomtsev-Petviashvili (KP) reduction method. Since the CSS equation is a special case of the four-component Hirota equation, our approach begins with the construction of two-bright-two-dark soliton solutions for the four-component Hirota equation. By imposing specific parameter constraints, these solutions are subsequently reduced to the bright-dark soliton solutions of the CSS equation. Finally, the dynamical behaviors of the one- and two-bright-dark soliton solutions are thoroughly analyzed and illustrated.