The Nonlinear Steepest Descent Approach for Long Time Behavior of the Two-component Coupled Sasa-Satsuma Equation with a $5 \times 5$ Lax Pair

Xiu-Bin Wang; Bo Han

doi:10.11650/tjm/200806

April, 2021 The Nonlinear Steepest Descent Approach for Long Time Behavior of the Two-component Coupled Sasa-Satsuma Equation with a $5 \times 5$ Lax Pair

Xiu-Bin Wang, Bo Han

Author Affiliations +

Taiwanese J. Math. 25(2): 381-407 (April, 2021). DOI: 10.11650/tjm/200806

Abstract

Under investigation in this work is the coupled Sasa-Satsuma equation, which can describe the propagations of two optical pulse envelopes in birefringent fibers. The Riemann-Hilbert problem for the equation is formulated on the basis of the corresponding $5 \times 5$ matrix spectral problem, which allows us to present a suitable representation for the solution of the equation. Then the Deift-Zhou steepest descent method is used to analyze the long time behavior of the coupled Sasa-Satsuma equation.

Funding Statement

This work is supported by the National Natural Science Foundation of China under Grant No. 11871180.

Acknowledgments

We express our sincere thanks to the editor and reviewer for their valuable comments.

Citation

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Xiu-Bin Wang. Bo Han. "The Nonlinear Steepest Descent Approach for Long Time Behavior of the Two-component Coupled Sasa-Satsuma Equation with a $5 \times 5$ Lax Pair." Taiwanese J. Math. 25 (2) 381 - 407, April, 2021. https://doi.org/10.11650/tjm/200806