Sergeev, Sergey M. Classical integrable field theories in discrete \((2+1)\)-dimensional spacetime. (English) Zbl 1177.35048 J. Phys. A, Math. Theor. 42, No. 29, Article ID 295206, 19 p. (2009). Summary: We study the ‘circular net’ (discrete orthogonal net) equations for the angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of the Lagrangian density. There are four distinct regimes for fields and spectral parameters classified by four types of spherical or hyperbolic triangles. Nonzero external spectral parameters provide the existence of field-theoretical ground states and soliton excitations. Spectral parameters of a spherical triangle correspond to a statistical mechanics; spectral parameters of hyperbolic triangles correspond to three different field theories with massless anisotropic dispersion relations. Cited in 2 Documents MSC: 35C05 Solutions to PDEs in closed form 35Q51 Soliton equations 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics 81T99 Quantum field theory; related classical field theories Keywords:circular net equations; conic net equations; solitons; spectral parameters PDFBibTeX XMLCite \textit{S. M. Sergeev}, J. Phys. A, Math. Theor. 42, No. 29, Article ID 295206, 19 p. (2009; Zbl 1177.35048) Full Text: DOI arXiv