Reduction of differential equations with symmetries

A method for constructing group-invariant solutions of differential equations is described. At the foundation of the method lies a reduction of the dimension of the base of a bundle of $k$-jets of functions $J^k(M^n,R^1)$ by means of a passage to the manifolds of orbits of the contact action of the Lie group of partial symmetries of the differential equation. Only the orbits of a certain submanifold of $J^k(M^n,R^1)$ are considered, an extension of an involutive system of first-order differential equations associated with the action of the group.
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