Some families of exact solutions of the equations of two-dimensional shallow water theory

Results are presented of a study of the exact solutions of the equations of two-dimensional unsteady and steady shallow water theory, based on the group properties of these equations. The first part presents the group properties of the equations in question; the second part presents the invariant solutions of these equations.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 10, No. 6, pp. 62–71, November–December, 1969.The author wishes to thank L. V. Ovsyannikov and N. Kh. Ibragimov for valuable guidance in carrying out this study.