Asymptotic, Algebraic and Geometric Aspects of Integrable Systems

1. Front Matter

   Pages i-viii

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2. Quadrangular Sets in Projective Line and in Moebius Space, and Geometric Interpretation of the Non-commutative Discrete Schwarzian Kadomtsev–Petviashvili Equation

   • Adam Doliwa, Jarosław Kosiorek

   Pages 1-15

3. Complexity and Integrability in 4D Bi-rational Maps with Two Invariants

   • Giorgio Gubbiotti, Nalini Joshi, Dinh Thi Tran, Claude-Michel Viallet

   Pages 17-36

4. A Non-linear Relation for Certain Hypergeometric Functions

   • Gerd Schmalz, Vladimir Ezhov

   Pages 37-41

5. An Algebraically Stable Variety for a Four-Dimensional Dynamical System Reduced from the Lattice Super-KdV Equation

   • Adrian Stefan Carstea, Tomoyuki Takenawa

   Pages 43-53

6. Opers for Higher States of the Quantum Boussinesq Model

   • Davide Masoero, Andrea Raimondo

   Pages 55-78

7. Nonsingular Rational Solutions to Integrable Models

   • Gegenhasi, Xing-Biao Hu, Shi-Hao Li, Bao Wang

   Pages 79-99

8. Stokes Phenomenon Arising in the Confluence of the Gauss Hypergeometric Equation

   • Calum Horrobin, Marta Mazzocco

   Pages 101-158

9. Periodic Trajectories of Ellipsoidal Billiards in the 3-Dimensional Minkowski Space

   • Vladimir Dragović, Milena Radnović

   Pages 159-174

10. Analogues of Kahan’s Method for Higher Order Equations of Higher Degree

    • A. N. W. Hone, G. R. W. Quispel

    Pages 175-189

11. On Some Explicit Representations of the Elliptic Painlevé Equation

    • Masatoshi Noumi

    Pages 191-212

12. On the Lattice Potential KP Equation

    • Cewen Cao, Xiaoxue Xu, Da-jun Zhang

    Pages 213-237

This proceedings volume gathers together selected works from the 2018 “Asymptotic, Algebraic and Geometric Aspects of Integrable Systems” workshop that was held at TSIMF Yau Mathematical Sciences Center in Sanya, China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems.


The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas.


This volume's articles reflect these exchanges  and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.

• discrete Painleve equations
• integrable lattices
• special and global behavior of solutions
• resolution and asymptotic analysis of initial of value space
• symmetries and geometry of discrete equations
• representation theory
• exactly solvable models
• theory of special functions
• combinatorial geometry

• School of Mathematics, University of Leeds, Leeds, UK

  Frank Nijhoff

• College of Science and Engineering, Flinders at Tonsley, Adelaide, Australia

  Yang Shi

• Department of Mathematics, Shanghai University, Shanghai, China

  Da-jun Zhang

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