Integrable Systems · Sato Theory · ASDYM · AI-assisted Research
Welcome to my personal academic homepage. I am a researcher working at the intersection of integrable systems, gauge field theory, and geometric analysis. My current work focuses on the mathematical structures underlying soliton equations, anti-self-dual Yang–Mills theory, Sato theory, and related algebraic and geometric methods. This website collects my publications, research notes, talks, and ongoing projects, including my recent interests in AI-assisted mathematical research.
Integrable Systems · Sato Theory · ASDYM · AI-assisted Research
I study the mathematical structures behind integrable systems and anti-self-dual Yang–Mills theory, while exploring thoughtful uses of AI in mathematical research.
Current position
Lecturer
Institution
Ningbo UniversityNingboChina 🇨🇳
Integrable systemsSato theoryASDYMAI-assisted research
My research lies in the area of integrable systems and their connections with geometry and mathematical physics. I am particularly interested in soliton equations, Sato theory, Cauchy matrix methods, and anti-self-dual Yang–Mills theory, with an emphasis on the algebraic and geometric structures behind integrable hierarchies.
Research focus · 02
AI-assisted workflows
In addition to my mathematical research, I am exploring how AI-assisted workflows can support mathematical writing, literature organization, symbolic computation, and the construction of personal research systems. I see these tools not as replacements for mathematical thinking, but as new ways to organize, test, and develop ideas.
Academic path
Education & appointments
The current position is listed first, followed by overseas experience and education.
@misc{LiMarunoZhang2026Unified,
title = {A unified approach to the AKNS, DNLS, KP and mKP hierarchies in the anti-self-dual Yang-Mills reduction},
author = {Shangshuai Li and Ken-ichi Maruno and Da-jun Zhang},
year = {2026},
eprint = {2603.23060},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2603.23060},
}
@article{LiLiuZhang2025FokasLenells,
title = {From the self-dual Yang-Mills equation to the Fokas-Lenells equation},
author = {Shangshuai Li and Shuzhi Liu and Da-jun Zhang},
year = {2025},
journal = {Studies in Applied Mathematics},
volume = {155},
number = {4},
eid = {e70126},
doi = {10.1111/sapm.70126},
url = {https://doi.org/10.1111/sapm.70126},
eprint = {2411.10807},
archivePrefix = {arXiv},
}
Published research · 2025
Soliton resonances in four dimensional Wess-Zumino-Witten model
@article{LiZhang2025Direct,
title = {Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces},
author = {Shangshuai Li and Da-jun Zhang},
year = {2025},
journal = {Journal of Geometry and Physics},
volume = {207},
eid = {105351},
doi = {10.1016/j.geomphys.2024.105351},
url = {https://doi.org/10.1016/j.geomphys.2024.105351},
eprint = {2403.06055},
archivePrefix = {arXiv},
}
Published research · 2024
On the extended 2-dimensional Toda lattice models
Conghan Wang, Shangshuai Li, Da-jun Zhang
Theoretical and Mathematical Physics, 221(3), 2049-2061, 2024
@article{WangLiZhang2024Toda,
title = {On the extended 2-dimensional Toda lattice models},
author = {Conghan Wang and Shangshuai Li and Da-jun Zhang},
year = {2024},
journal = {Theoretical and Mathematical Physics},
volume = {221},
number = {3},
pages = {2049-2061},
doi = {10.1134/S0040577924120043},
url = {https://link.springer.com/article/10.1134/S0040577924120043},
}
Published research · 2024
Nonisospectral equations from the Cauchy matrix approach
Alemu Yilma Tefera, Shangshuai Li, Da-jun Zhang
Reports on Mathematical Physics, 94(1), 47-72, 2024
@article{TeferaLiZhang2024NonisospectralEquations,
title = {Nonisospectral equations from the Cauchy matrix approach},
author = {Alemu Yilma Tefera and Shangshuai Li and Da-jun Zhang},
year = {2024},
journal = {Reports on Mathematical Physics},
volume = {94},
number = {1},
pages = {47-72},
doi = {10.1016/S0034-4877(24)00055-7},
url = {https://www.sciencedirect.com/science/article/pii/S0034487724000557},
}
Published research · 2024
Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations
Alemu Yilma Tefera, Shangshuai Li, Da-jun Zhang
Communications in Theoretical Physics, 76(5), 055001, 2024
@article{TeferaLiZhang2024NLS,
title = {Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations},
author = {Alemu Yilma Tefera and Shangshuai Li and Da-jun Zhang},
year = {2024},
journal = {Communications in Theoretical Physics},
volume = {76},
number = {5},
eid = {055001},
doi = {10.1088/1572-9494/ad35b1},
url = {https://iopscience.iop.org/article/10.1088/1572-9494/ad35b1/meta},
}
Published research · 2024
Cauchy matrix structure and solutions of the spin-1 Gross-Pitaevskii equations
Shangshuai Li, Da-jun Zhang
Communications in Nonlinear Science and Numerical Simulation, 129, 107705, 2024
Status
Published
Year
2024
Venue
Communications in Nonlinear Science and Numerical Simulation
@article{LiZhang2024Spin1GrossPitaevskii,
title = {Cauchy matrix structure and solutions of the spin-1 Gross-Pitaevskii equations},
author = {Shangshuai Li and Da-jun Zhang},
year = {2024},
journal = {Communications in Nonlinear Science and Numerical Simulation},
volume = {129},
eid = {107705},
doi = {10.1016/j.cnsns.2023.107705},
url = {https://www.sciencedirect.com/science/article/pii/S1007570423006263},
}
Published research · 2023
Solutions to the SU(N) self-dual Yang-Mills equation
@article{ShiLiZhang2022NoncommutativeKP,
title = {Cauchy matrix approach to the noncommutative Kadomtsev-Petviashvili equation with self-consistent sources},
author = {Zhihao Shi and Shangshuai Li and Da-jun Zhang},
year = {2022},
journal = {Theoretical and Mathematical Physics},
volume = {213},
number = {3},
pages = {1686-1697},
doi = {10.1134/S0040577922120030},
url = {https://link.springer.com/article/10.1134/S0040577922120030},
}
Published research · 2022
Cauchy matrix approach to the SU(2) self-dual Yang-Mills equation
@article{LiQuYiZhang2022Cauchy,
title = {Cauchy matrix approach to the SU(2) self-dual Yang-Mills equation},
author = {Shangshuai Li and Changzheng Qu and Xiangxuan Yi and Da-jun Zhang},
year = {2022},
journal = {Studies in Applied Mathematics},
volume = {148},
number = {4},
pages = {1703-1721},
doi = {10.1111/sapm.12488},
url = {https://doi.org/10.1111/sapm.12488},
eprint = {2112.06408},
archivePrefix = {arXiv},
}
Published research · 2021
Symmetric discrete AKP and BKP equations
Shangshuai Li, Frank W. Nijhoff, Ying-ying Sun, Da-jun Zhang
Journal of Physics A: Mathematical and Theoretical, 54(7), 075201, 2021
Status
Published
Year
2021
Venue
Journal of Physics A: Mathematical and Theoretical
@article{LiNijhoffSunZhang2021Symmetric,
title = {Symmetric discrete AKP and BKP equations},
author = {Shangshuai Li and Frank W. Nijhoff and Ying-ying Sun and Da-jun Zhang},
year = {2021},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {54},
number = {7},
eid = {075201},
doi = {10.1088/1751-8121/abd998},
url = {https://doi.org/10.1088/1751-8121/abd998},
eprint = {2009.04054},
archivePrefix = {arXiv},
}
2026 Talks
2025 Talks
2024 Talks
Seminar or conference talk · 2026
On soliton-preserving anti-self-dual Yang-Mills reductions
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