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Two-dimensional exactly and completely integrable dynamical systems

Monopoles, instantons, dual models, relativistic strings, lund-regge model, generalized toda lattice, etc.

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Abstract

An investigation of two-dimensional exactly and completely integrable dynamical systems associated with the local part of an arbitrary Lie algebra\(\mathfrak{g}\) whose grading is consistent with an arbitrary integral embedding of 3d-subalgebra in\(\mathfrak{g}\) has been carried out. We have constructed in an explicit form the corresponding systems of nonlinear partial differential equations of the second order and obtained their general solutions in the sense of a Goursat problem. A method for the construction of a wide class of infinite-dimensional Lie algebras of finite growth has been proposed.

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Authors and Affiliations

  1. Institute for High Energy Physics, Protvino, Serpukhov, P.O. Box 35, SU-142284, Moscow Region, USSR

    A. N. Leznov & M. V. Saveliev

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  1. A. N. Leznov
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  2. M. V. Saveliev
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Communicated by Ya. G. Sinai

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Leznov, A.N., Saveliev, M.V. Two-dimensional exactly and completely integrable dynamical systems. Commun.Math. Phys. 89, 59–75 (1983). https://doi.org/10.1007/BF01219526

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