Lecturer, Ningbo University JSPS Fellow, Nagoya University
Abstract. My research concerns the algebraic and geometric structures of integrable systems and their connections with mathematical physics. I focus on Sato theory, Cauchy matrix methods, (anti-)self-dual Yang–Mills equations, and exact soliton solutions.
KeywordsSato theoryCauchy matrix approachdirect linearization(anti-)self-dual Yang–MillsWard conjecturesolitons & resonances
Three connected themes: how lower-dimensional integrable hierarchies sit inside the (anti-)self-dual Yang–Mills equations, the constructive Cauchy-matrix machinery that produces their solutions, and the soliton structures that result.
I study the connections between (anti-)self-dual Yang–Mills equations and lower-dimensional integrable hierarchies. Current work includes Sato-theoretic constructions, dimensional reductions, and examples related to the Ward conjecture.
Key paperSato-theoretic construction of the ASDYM hierarchyCauchy matrix structures and direct linearization provide constructive approaches to Yang–Mills equations and related integrable systems. I am interested in the algebraic structures underlying these methods and the exact solutions they produce.
Key paperDirect linearization of the SU(2) ASDYM equationI investigate exact soliton solutions and resonance phenomena in four-dimensional Wess–Zumino–Witten models. Topics include multiple-pole solutions, V-shape solitons, and the relationship between Cauchy matrix methods and binary Darboux transformations.
Key paperSoliton resonances in the WZW modelNodes represent equations, solution families and constructions studied in the papers below; edges connect them to their research frameworks. Hover to see the papers, click to filter the publication list.
Journal articles, preprints and proceedings, newest first. Citation counts from Google Scholar.
Shangshuai Li, Ken-ichi Maruno, Da-jun Zhang
Derives related (2+1)-dimensional NLS, derivative NLS and Heisenberg ferromagnet equations from one ASDYM constraint, with explicit gauge transformations and Cauchy-matrix solutions.
Shangshuai Li
Establishes a local exact correspondence between quasi-Wronskian and quasi-Grammian constructions for complex 2×2 ASDYM fields through a shared matrix-polynomial interpolation problem, showing that both produce identical gauge potentials.
Shangshuai Li, Da-jun Zhang
A Sato-theoretic dressing framework for the ASDYM hierarchy, with classical integrable hierarchies recovered by dimensional reduction.
Shangshuai Li, Ken-ichi Maruno, Da-jun Zhang
A common ASDYM reduction framework for the AKNS, DNLS, KP and mKP hierarchies.
Zichen Huang, Shangshuai Li, Da-jun Zhang
Applied Mathematics Letters
Shows how the entire Korteweg–de Vries hierarchy and its solutions can be formulated in the Cauchy matrix approach, extendable to other integrable equations.
Taisei Wakamatsu, Ken-ichi Maruno, Shangshuai Li, Da-jun Zhang
RIMS Kokyuroku
Japanese-language RIMS Kôkyûroku proceedings article on elliptic soliton solutions of the Calogero–Bogoyavlenskii–Schiff equation.
Shangshuai Li, Shuzhi Liu, Da-jun Zhang
Studies in Applied Mathematics
A reduction from self-dual Yang–Mills equations to the Fokas–Lenells system through two Cauchy matrix schemes.
Shangshuai Li, Masashi Hamanaka, Shan-Chi Huang, Da-Jun Zhang
Physical Review D
Resonance soliton solutions in four-dimensional Wess–Zumino–Witten models, including multiple-pole and V-shape solutions.
Shangshuai Li, Da-jun Zhang
Journal of Geometry and Physics
Develops a direct linearization scheme from linear integral equations for the SU(2) ASDYM equation, reduced to Euclidean and two ultrahyperbolic spaces.
Conghan Wang, Shangshuai Li, Da-jun Zhang
Theoretical and Mathematical Physics
Studies an extended 2D Toda lattice via Cauchy matrices, viewing it as a negative-order member of the discrete KP hierarchy and bilinearizing it with one τ-function.
Alemu Yilma Tefera, Shangshuai Li, Da-jun Zhang
Reports on Mathematical Physics
Uses the Cauchy matrix approach with nonisospectral dispersion relations to construct explicit solutions of nonisospectral KdV, modified KdV and sine-Gordon equations.
Alemu Yilma Tefera, Shangshuai Li, Da-jun Zhang
Communications in Theoretical Physics
Derives three non-isospectral nonlinear Schrödinger equations and explicit solutions via the Cauchy matrix approach, illustrating non-isospectral effects on soliton dynamics.
Shangshuai Li, Da-jun Zhang
Communications in Nonlinear Science and Numerical Simulation
Derives a 2×2 matrix NLS equation via Cauchy matrices as an unreduced spin-1 BEC model, reducing to classical and nonlocal spin-1 Gross–Pitaevskii equations.
Shangshuai Li, Changzheng Qu, Da-jun Zhang
Physica D: Nonlinear Phenomena
Derives solutions of the SU(N) self-dual Yang–Mills equation for arbitrary N from two Sylvester-equation Cauchy matrix schemes (KP and AKNS types).
Zhihao Shi, Shangshuai Li, Da-jun Zhang
Theoretical and Mathematical Physics
Constructs matrix solutions of the noncommutative KP equation with self-consistent sources from a Sylvester equation, without quasideterminants; a reduction gives solutions of the matrix Mel'nikov model.
Shangshuai Li, Changzheng Qu, Xiangxuan Yi, Da-jun Zhang
Studies in Applied Mathematics
Develops the Cauchy matrix approach for the SU(2) self-dual Yang–Mills equation, obtaining a broad class of explicit solutions under Yang's formulation.
Shangshuai Li, Frank W. Nijhoff, Ying-ying Sun, Da-jun Zhang
Journal of Physics A: Mathematical and Theoretical
Shows that the discrete BKP equation is a combination of the discrete AKP equation and its reflections for symmetric τ-functions, yielding a discrete BKP equation with elliptic coefficients.
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Talks and poster presentations, with materials where available, and workshops co-organized.
From Nonlinear Wave to Integrable System 2026 · Kunibiki Messe, Matsue, Japan
Integrability, Self-Duality, and Twistor Theory · Nagoya University, Nagoya, Japan
Nagoya University, Nagoya, Japan
with Masashi Hamanaka and Shintaro Yanagida
Mini workshop on ASD Yang-Mills Equations · Nagoya University, Nagoya, Japan
Nagoya University, Nagoya, Japan
with Masashi Hamanaka and Shintaro Yanagida
Development and Applications of New Mathematical Methods for Discrete Integrable Systems · Hotel Stay Inn Nanokamachi, Yamagata, Japan
Representation Theory, Integrable Systems and Related Topics · BIMSA, Beijing, China
Waseda Workshop on Discrete Integrable Systems and Related Topics · Waseda University, Tokyo, Japan
From Nonlinear Wave to Integrable System 2024 · Fukui University, Fukui, Japan
Nagoya Math-Phys Seminar · Nagoya University, Nagoya, Japan
International Seminar-Type Online Workshop on Noncommutative Integrable Systems · Zoom (online)
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Computed from the publication list: the closer the orbit, the more joint papers. Hover a name to light up the shared work.
14 co-authors across 17 papers.
For questions about the papers, preprint requests, seminar invitations or collaboration, email is the most direct route.