Dark Soliton and Breather Solutions to the Coupled Sasa–Satsuma Equation

Authors

Guangxiong Zhang
Changyan Shi, The University of Texas Rio Grande Valley
Chengfa Wu
Bao-Feng Feng, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2025

Abstract

We construct dark soliton and breather solutions to the coupled Sasa–Satsuma (CSS) equation under nonzero boundary condition. First, the CSS equation is bilinearized into six equations by introducing three auxiliary tau functions. Then, it is shown that these six bilinear equations can be reduced from a set of 33 bilinear equations in the Kadomtsev–Petviashvili (KP)-Toda hierarchy including the discrete KP equation. As a result, two alternative determinant forms of the dark soliton and breather solutions, along with their mixed type, are derived. The rich structures and the dynamical behaviors of both dark and breather solutions are analyzed and illustrated. Especially, the resonant breather and resonant dark soliton solutions are found in the same determinant form.

Comments

Copyright © 2024, The Author(s), under exclusive licence to Springer Science Business Media, LLC, part of Springer Nature

https://rdcu.be/d562U

Recommended Citation

Zhang, Guangxiong, Changyan Shi, Chengfa Wu, and Bao-Feng Feng. "Dark Soliton and Breather Solutions to the Coupled Sasa–Satsuma Equation." Journal of Nonlinear Science 35, no. 1 (2025): 7. https://doi.org/10.1007/s00332-024-10100-z

Publication Title

Journal of Nonlinear Science

DOI

https://doi.org/10.1007/s00332-024-10100-z