Painlevé asymptotics for the coupled Sasa-Satsuma equation
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- by Nan Liu, Zhong-Zhou Lan and Jia-Dong Yu;
- Proc. Amer. Math. Soc. 151 (2023), 3763-3778
- DOI: https://doi.org/10.1090/proc/16344
- Published electronically: June 6, 2023
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Abstract:
We compute the long-time asymptotics of the solution to the Cauchy problem for coupled Sasa-Satsuma equation on the line with decaying initial data. By performing a nonlinear steepest descent arguments for an associated $5\times 5$ matrix Riemann–Hilbert problem, it turns out that in the sector $|x/t^{1/3}|\leq N$, $N$ constant, the asymptotics can be expressed in terms of the solution of a coupled modified Painlevé II equation, which is related to a $5\times 5$ matrix Riemann–Hilbert problem.References
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Bibliographic Information
- Nan Liu
- Affiliation: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, People’s Republic of China; Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing 210044, People’s Republic of China; and Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and Technology, Nanjing 210044, People’s Republic of China
- Email: ln10475@163.com
- Zhong-Zhou Lan
- Affiliation: School of Computer Information Management, Inner Mongolia University of Finance and Economics, Hohhot 010070, People’s Republic of China
- Email: zhongzhou_lan@163.com
- Jia-Dong Yu
- Affiliation: College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian 271016, People’s Republic of China
- ORCID: 0000-0003-2042-9923
- Email: yujiadong@sdfmu.edu.cn
- Received by editor(s): July 23, 2022
- Received by editor(s) in revised form: October 3, 2022, and October 25, 2022
- Published electronically: June 6, 2023
- Additional Notes: The third author is the corresponding author.
The first author was supported by Natural Science Foundation of Jiangsu Province under Grant No. BK20220434, the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 22KJB110002, and the Startup Foundation for Introducing Talent of NUIST under Grant No. 2022r028. The second author was supported by the National Natural Science Foundation of China under Grant No. 12161061, the Special Fund for the Local Science and Technology Development of the Central Government under Grant No. 2020ZY0014, the Natural Science Foundation of Inner Mongolia under Grant No. 2021MS01022, the 2022 Scientific Research and Innovation Fund of Inner Mongolia University of Finance and Economics, the Fundamental Research Funds for the Inner Mongolia Normal University under Grant No. 2022JBBJ008 and the Talent Development Fund of Inner Mongolia. - Communicated by: Mourad Ismail
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 3763-3778
- MSC (2020): Primary 35Q15; Secondary 37K40
- DOI: https://doi.org/10.1090/proc/16344
- MathSciNet review: 4607622