\(\text{Q}_4\): Integrable master equation related to an elliptic curve. (English) Zbl 1081.37038
It is well known that one of the most fascinating part of the theory of \(2\)-dimensional integrable systems is the study of the systems with the spectral parameter on an elliptic curve. These include Landau-Lifshitz equations, Krichever-Novikov equations, elliptic Toda lattice equations and elliptic Ruijsenaars-Toda lattice equations. Here, the authors explain how all these equations can be unified on the basis of a single equation \(\text{Q}_4\) introduced by the first author some years ago [Int. Math. Res. Not. 1998, 1–4 (1998; Zbl 0895.35089)].
Reviewer: Mircea Puta (Timişoara)
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 14H70 | Relationships between algebraic curves and integrable systems |
| 37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
| 37K60 | Lattice dynamics; integrable lattice equations |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
