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Shangshuai Li

Integrable systems · ASDYM · AI-assisted research

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Shangshuai Li

Integrable Systems · Sato Theory · ASDYM · AI-assisted Research

Research profile

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 🇨🇳

Research areas

Integrable systemsSato theoryASDYMAI-assisted research

Google Scholar↗ResearchGate↗ORCID↗

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

2025-present
Lecturer
Ningbo UniversityNingboChina 🇨🇳

Overseas Experience3 entries

2025-present
JSPS Fellow
Nagoya UniversityNagoyaJapan 🇯🇵
Host: Masashi Hamanaka
2024-2025
Visiting Research Fellow
Waseda UniversityTokyoJapan 🇯🇵
Host: Kenichi Maruno
2019
Exchange Student
Latrobe UniversityVictoriaAustralia 🇦🇺
Host: Peter van der Kamp

Education2 entries

2019-2025
Doctor of Science
Shanghai UniversityShanghaiChina 🇨🇳
Advisor: Da-jun Zhang
Thesis: Direct method to the self-dual Yang-Mills equation
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

Selected project

Academic Oracle

A three-card, tarot-inspired research reflection tool for drafts, proofs, submissions, collaborations, and uncertain methods.

Built through AI-assisted coding

Status: Live
Year: 2026
Runs: Locally in your browser

AstroTypeScriptInteractive narrative

More experiments will appear here as they become ready to use.

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
arXiv: 2603.23060
PDF: Open in PDF Reader

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
DOI: 10.1016/j.aml.2025.109726

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
DOI: 10.1111/sapm.70126
arXiv: 2411.10807
PDF: Open in PDF Reader

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
DOI: 10.1103/PhysRevD.111.086023
arXiv: 2501.08250
PDF: Open in PDF Reader

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
DOI: 10.1016/j.geomphys.2024.105351
arXiv: 2403.06055
PDF: Open in PDF Reader

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
DOI: 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
DOI: 10.1016/S0034-4877(24)00055-7

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
DOI: 10.1088/1572-9494/ad35b1

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
DOI: 10.1016/j.cnsns.2023.107705

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
DOI: 10.1016/j.physd.2023.133828
arXiv: 2211.08574
PDF: Open in PDF Reader

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
DOI: 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
DOI: 10.1111/sapm.12488
arXiv: 2112.06408
PDF: Open in PDF Reader

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
DOI: 10.1088/1751-8121/abd998
arXiv: 2009.04054
PDF: Open in PDF Reader

Years

2026 Talks

2025 Talks

2024 Talks

Seminar or conference talk · 2026

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

March 22, 2026

Category: Talk
Year: 2026
Date: March 22, 2026
Event: Development and Applications of New Mathematical Methods for Discrete Integrable Systems
Location: Yamagata University, Yamagata, Japan
Slides: Open in PDF Reader

Seminar or conference talk · 2025

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

January 9, 2025

Category: Talk
Year: 2025
Date: January 9, 2025
Event: Waseda Workshop on Discrete Integrable Systems and Related Topics
Location: Waseda University, Tokyo, Japan
Slides: Open in PDF Reader

Seminar or conference talk · 2024

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

November 8, 2024

Category: Talk
Year: 2024
Date: November 8, 2024
Event: From Nonlinear Wave to Integrable System 2024
Location: Fukui University, Fukui, Japan
Slides: Open in PDF Reader

Seminar or conference talk · 2024

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

March 15, 2024

Category: Talk
Year: 2024
Date: March 15, 2024
Event: International Seminar-Type Online Workshop on Noncommutative Integrable Systems
Location: Nagoya University, Nagoya, Japan
Slides: Open in PDF Reader

Research Browser

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System Settings

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CatalogueAcademic Oracle

Runs locally in your browser

Mathematics

AI-assisted workflows

Lecturer

JSPS Fellow

Visiting Research Fellow

Exchange Student

Doctor of Science

Bachelor of Science

Contact

Academic Oracle

Website architecture refactored

Website launched

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

The KdV hierarchy: Cauchy matrix approach

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

Soliton resonances in four dimensional Wess-Zumino-Witten model

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

On the extended 2-dimensional Toda lattice models

Nonisospectral equations from the Cauchy matrix approach

Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations

Cauchy matrix structure and solutions of the spin-1 Gross-Pitaevskii equations

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

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

Cauchy matrix approach to the SU(2) self-dual Yang-Mills equation

Symmetric discrete AKP and BKP equations

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

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

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

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