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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...
The system of differential equations which describes the motion of continuum media of gas, liquid, Reiner-Rievling-type liquid, etc., is considered.
The recursion operator method for nonlinear evolution equations integrable by the inverse spectral transform method is discussed. This method enables us to present the integrable equations in a compact and convenient form and to construct the infinite-dimensional groups of general Bäcklund...
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