Geodesic
Reduction of differential equations with symmetries
Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 73-86.

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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. Bibliography: 7 titles. 
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E. M. Vorob'ev. Reduction of differential equations with symmetries. Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 73-86. http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a2/

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[7] Weinstein A., “Symplectic manifolds and their Lagrangian submanifolds”, Adv. Math., 6 (1971), 329–346 | DOI | MR | Zbl