Pohlmeyer’s transformation and the \((2+0)\) integrable equations of statistical physics. (English. Russian original) Zbl 0970.37055
J. Math. Sci., New York 100, No. 2, 2105-2115 (2000); translation from Zap. Nauchn. Semin. POMI 245, 149-164 (1997).
Author’s summary: Using the Pohlmeyer transformation in Euclidean space, we obtain an equation which provides the possibility of constructing a wide class of two-dimensional elliptic integrable systems. The problem of the gauge equivalence of these systems with the nonlinear sigma-model and the Getmanov and Bitsadze models is investigated. Exact solutions of some equations are constructed.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 82B23 | Exactly solvable models; Bethe ansatz |
Keywords:
two-dimensional elliptic integrable systems; gauge equivalence; nonlinear sigma-model; Getmanov and Bitsadze modelsReferences:
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