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

Shi, Changyan; Chen, Xiyao; Zhang, Guangxiong; Wu, Chengfa; Feng, Bao-Feng

IMA Journal of Applied MathematicsMay 8, 2026

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

Abstract

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.

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