Geodesic
The 2D motion of perfect fluid with a free surface
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 1, pp. 3-6.

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The 3D continuous subalgebra is used to searching new partially invariant solution of incompressible perfect fluid equations. It can be interpreted as a non-stationary motion of a plane layer with one free surface. The velocity field and pressure are determined in analytical form by using Lagrangian coordinates.
Keywords: perfect fluid, partially invariant solution, non-stationary motion, free surfaces. 
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Victor K. Andreev. The 2D motion of perfect fluid with a free surface. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 1, pp. 3-6. http://geodesic.mathdoc.fr/item/JSFU_2015_8_1_a0/

[1] A. A. Buchnev, “A Lie group admissible for the equations of an ideal incompressible fluid”, Dinamika Sploshnoy Sredy, 7, Novosibirsk, 1971, 212–214 (in Russian)

[2] A. D. Polyanin, V. F. Zaitsev, Handbook of nonlinear partial differential equations, CRC Press. Taylor and Francis Group, 2012, 942–949

[3] V. K. Andreev, O. V. Kaptsov, V. V. Pukhnachev, A. A. Rodionov, Application of GroupTheoretical Methods in Hydrodynamics, Kluwer Acad. Publ., Dordrecht–Boston–London, 2010