Nonlinear \(\sigma\)-model in a curved space, gauge equivalence, and exact solutions of \((2+0)\)-dimensional integrable equations. (English. Russian original) Zbl 1113.81095
Theor. Math. Phys. 115, No. 3, 619-638 (1998); translation from Teor. Mat. Fiz. 115, No. 3, 323-348 (1998).
Summary: We propose a nonlinear \(\sigma\)-model in a curved space as a general integrable elliptic model. We construct its exact solutions and obtain energy estimates near the critical point. We consider the Pohlmeyer transformation in Euclidean space and investigate the gauge equivalence conditions for a broad class of elliptic equations. We develop the inverse scattering transform method for the sinh-Gordon equation and evaluate its exact and asymptotic solutions.
MSC:
| 81T10 | Model quantum field theories |
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
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