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ShuAIence

A research desktop by Shangshuai Li.

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Shangshuai Li

Integrable systems · ASDYM · AI-assisted research
Welcome to ShuAIence
Blue orbit profile illustration for Shangshuai Li

Researching across mathematics and AI

Welcome to my research desktop

Shangshuai Li

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.

Google Scholar↗ResearchGate↗ORCID↗
Integrable systemsSato theoryASDYMAI-assisted research

© 2026 Shangshuai Li · Built as a personal research system.

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Talk slides and research papers stored on ShuAIence.

11 documents

Papers

Locally stored arXiv research papers

7
PDFA unified approach to the AKNS, DNLS, KP and mKP hierarchies in the anti-self-dual Yang-Mills reduction2026PDFFrom the self-dual Yang-Mills equation to the Fokas-Lenells equation2025PDFSoliton resonances in four dimensional Wess-Zumino-Witten model2025PDFDirect linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces2025PDFSolutions to the SU(N) self-dual Yang-Mills equation2023PDFCauchy matrix approach to the SU(2) self-dual Yang-Mills equation2022PDFSymmetric discrete AKP and BKP equations2021

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Seminar, workshop, and conference presentations

4
SLDOn soliton-preserving anti-self-dual Yang-Mills reductionsMarch 22, 2026SLDFrom self-dual Yang-Mills equation to Fokas-Lenells equationJanuary 9, 2025SLDCauchy matrix approach, Sylvester equation, self-dual Yang-Mills equation and their relationship with integrable systemNovember 8, 2024SLDSolutions to the SU(N) self-dual Yang-Mills equationMarch 15, 2024
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Blue orbit profile illustration for Shangshuai Li

Welcome to my research desktop

Shangshuai Li

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
Google Scholar↗ResearchGate↗ORCID↗

Researching across mathematics and AI

Research profile

Research at a glance

Research focus · 01

Mathematics

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.

Current Position1 entry
  1. 2025-present

    Lecturer

    Ningbo UniversityNingboChina 🇨🇳
Overseas Experience3 entries
  1. 2025-present

    JSPS Fellow

    Nagoya UniversityNagoyaJapan 🇯🇵

    Host: Masashi Hamanaka↗

  2. 2024-2025

    Visiting Research Fellow

    Waseda UniversityTokyoJapan 🇯🇵

    Host: Kenichi Maruno↗

  3. 2019

    Exchange Student

    Latrobe UniversityVictoriaAustralia 🇦🇺

    Host: Peter van der Kamp

Education2 entries
  1. 2019-2025

    Doctor of Science

    Shanghai UniversityShanghaiChina 🇨🇳

    Advisor: Da-jun Zhang

    Thesis: Direct method to the self-dual Yang-Mills equation

  2. 2015-2019

    Bachelor of Science

    Shanghai UniversityShanghaiChina 🇨🇳

Stay in touch

Contact

For research discussions, collaborations, and academic correspondence.

@ Email
lishangshuai [AT] shu.edu.cn
⌘ GitHub
github.com/lishangshuai ↗

© 2026 Shangshuai Li · Built as a personal research system.

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Academic Oracle

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Built through AI-assisted coding
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2026
Runs
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Years

2026 News

Research log · July 20, 2026

Website architecture refactored

We refactored the website's codebase into a macOS-inspired research desktop and added in-browser previews for locally hosted PDF documents.

Category
News
Year
2026
Date
July 20, 2026

Research log · June 30, 2026

Website launched

We launched this website today.

Category
News
Year
2026
Date
June 30, 2026

Years

2026 Publications

2025 Publications

2024 Publications

2023 Publications

2022 Publications

2021 Publications

Preprint · 2026

A unified approach to the AKNS, DNLS, KP and mKP hierarchies in the anti-self-dual Yang-Mills reduction

Shangshuai Li, Ken-ichi Maruno, Da-jun Zhang

arXiv preprint, 2026

Status
Preprint
Year
2026
Venue
arXiv preprint
arXivPDF
▾BibTeX
@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},
}

Published research · 2026

The KdV hierarchy: Cauchy matrix approach

Zichen Huang, Shangshuai Li, Da-jun Zhang

Applied Mathematics Letters, 172, 109726, 2026

Status
Published
Year
2026
Venue
Applied Mathematics Letters
Published version
▾BibTeX
@article{HuangLiZhang2026KdV,
  title = {The KdV hierarchy: Cauchy matrix approach},
  author = {Zichen Huang and Shangshuai Li and Da-jun Zhang},
  year = {2026},
  journal = {Applied Mathematics Letters},
  volume = {172},
  eid = {109726},
  doi = {10.1016/j.aml.2025.109726},
  url = {https://www.sciencedirect.com/science/article/pii/S0893965925002769},
}

Published research · 2025

From the self-dual Yang-Mills equation to the Fokas-Lenells equation

Shangshuai Li, Shuzhi Liu, Da-jun Zhang

Studies in Applied Mathematics, 155(4), e70126, 2025

Status
Published
Year
2025
Venue
Studies in Applied Mathematics
Published versionarXivPDF
▾BibTeX
@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

Shangshuai Li, Masashi Hamanaka, Shan-Chi Huang, Da-Jun Zhang

Physical Review D, 111(8), 086023, 2025

Status
Published
Year
2025
Venue
Physical Review D
Published versionarXivPDF
▾BibTeX
@article{LiHamanakaHuangZhang2025WZW,
  title = {Soliton resonances in four dimensional Wess-Zumino-Witten model},
  author = {Shangshuai Li and Masashi Hamanaka and Shan-Chi Huang and Da-Jun Zhang},
  year = {2025},
  journal = {Physical Review D},
  volume = {111},
  number = {8},
  eid = {086023},
  doi = {10.1103/PhysRevD.111.086023},
  url = {https://doi.org/10.1103/PhysRevD.111.086023},
  eprint = {2501.08250},
  archivePrefix = {arXiv},
}

Published research · 2025

Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces

Shangshuai Li, Da-jun Zhang

Journal of Geometry and Physics, 207, 105351, 2025

Status
Published
Year
2025
Venue
Journal of Geometry and Physics
Published versionarXivPDF
▾BibTeX
@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

Status
Published
Year
2024
Venue
Theoretical and Mathematical Physics
Published version
▾BibTeX
@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

Status
Published
Year
2024
Venue
Reports on Mathematical Physics
Published version
▾BibTeX
@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

Status
Published
Year
2024
Venue
Communications in Theoretical Physics
Published version
▾BibTeX
@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
Published version
▾BibTeX
@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

Shangshuai Li, Changzheng Qu, Da-jun Zhang

Physica D: Nonlinear Phenomena, 453, 133828, 2023

Status
Published
Year
2023
Venue
Physica D: Nonlinear Phenomena
Published versionarXivPDF
▾BibTeX
@article{LiQuZhang2023SUN,
  title = {Solutions to the SU(N) self-dual Yang-Mills equation},
  author = {Shangshuai Li and Changzheng Qu and Da-jun Zhang},
  year = {2023},
  journal = {Physica D: Nonlinear Phenomena},
  volume = {453},
  eid = {133828},
  doi = {10.1016/j.physd.2023.133828},
  url = {https://doi.org/10.1016/j.physd.2023.133828},
  eprint = {2211.08574},
  archivePrefix = {arXiv},
}

Published research · 2022

Cauchy matrix approach to the noncommutative Kadomtsev-Petviashvili equation with self-consistent sources

Zhihao Shi, Shangshuai Li, Da-jun Zhang

Theoretical and Mathematical Physics, 213(3), 1686-1697, 2022

Status
Published
Year
2022
Venue
Theoretical and Mathematical Physics
Published version
▾BibTeX
@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

Shangshuai Li, Changzheng Qu, Xiangxuan Yi, Da-jun Zhang

Studies in Applied Mathematics, 148(4), 1703-1721, 2022

Status
Published
Year
2022
Venue
Studies in Applied Mathematics
Published versionarXivPDF
▾BibTeX
@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
Published versionarXivPDF
▾BibTeX
@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},
}

Years

2026 Talks

2025 Talks

2024 Talks

Seminar or conference talk · 2026

On soliton-preserving anti-self-dual Yang-Mills reductions

March 22, 2026

Development and Applications of New Mathematical Methods for Discrete Integrable Systems

YamagataJapan 🇯🇵
Category
Talk
Year
2026
Date
March 22, 2026
Slides

Seminar or conference talk · 2025

From self-dual Yang-Mills equation to Fokas-Lenells equation

January 9, 2025

Waseda Workshop on Discrete Integrable Systems and Related Topics

Waseda UniversityTokyoJapan 🇯🇵
Category
Talk
Year
2025
Date
January 9, 2025
Slides

Seminar or conference talk · 2024

Cauchy matrix approach, Sylvester equation, self-dual Yang-Mills equation and their relationship with integrable system

November 8, 2024

From Nonlinear Wave to Integrable System 2024

Fukui UniversityFukuiJapan 🇯🇵
Category
Talk
Year
2024
Date
November 8, 2024
Slides

Seminar or conference talk · 2024

Solutions to the SU(N) self-dual Yang-Mills equation

March 15, 2024

International Seminar-Type Online Workshop on Noncommutative Integrable Systems

Nagoya UniversityNagoyaJapan 🇯🇵
Category
Talk
Year
2024
Date
March 15, 2024
Slides
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