Abstract
This survey is devoted to a consistent exposition of the group-algebraic methods for the integration of systems of nonlinear partial differential equations possessing a nontrivial internal symmetry algebra. Samples of exactly and completely integrable wave and evolution equations are considered in detail, including the generalized (periodic and finite nonperiodic) Toda lattice, nonlinear Schrodinger, Korteweg-de Vries, Lotka-Volterra equations, etc.). For exactly integrable systems, the general solutions of the Cauchy and Goursat problems are given in an explicit form, while for completely integrable systems an effective method for the construction of their soliton solutions is developed.
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