Soliton Solutions to the Coupled Sasa-Satsuma-mKdV Equation

Authors

• Changyan Shi, The University of Texas Rio Grande Valley
• Bao-Feng Feng, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-1-2026

Abstract

We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-modified Korteweg-de Vries (Sasa-Satsuma-mKdV) equation using the Kadomtsev–Petviashvili reduction method. Under zero, nonzero and mixed boundary conditions, we derive four distinct classes of soliton solutions: bright–bright, dark–dark, bright–dark, and dark–bright. These solutions are derived from the vector Hirota equation, for which the bright, dark, and bright–dark soliton solutions are provided in the Appendix. We perform asymptotic analysis of soliton collisions for each class of solutions. Inelastic collisions are observed between bright–bright solitons. In the dark–dark case, the soliton structures are similar to those of the Sasa-Satsuma equation which include double-hole, Mexican hat and anti-Mexican hat solutions. The collision between these solitons and kink solitons and the resonances between dark–dark solitons and breather–breather are new phenomena found in the coupled Sasa-Satsuma-mKdV equation.

Comments

https://onlinelibrary.wiley.com/share/ER9CK8A8T5ZFARVRHGMQ?target=10.1111/sapm.70292

Recommended Citation

https://doi.org/10.1111/sapm.70292

Publication Title

Studies in Applied Mathematics

DOI

10.1111/sapm.70292