Transformations of the equivalence of the movement equations of a twodimensional layer of ideal liquid

Group properties of the equations of the movement of a two-dimensional layer of ideal liquid concerning the function describing thickness of a layer of liquid under free border are investigated. The equations are written down in the modified variables that allowed to record area borders on a variable. The task of the group analysis is set, the continued operator on the first derivatives is found, using the criterion of invariancy, the defining equations are constructed and equivalence transformations for system of the equations (1)—(4) are found. Transformations of equivalence are such transformations which keep structure of initial system of the equations. It is proved that the equivalence transformations for the system (5)—(8) have the structure of the infinite-dimensional group of transformations. This task has applied the value for finding of exact decisions of systems of the differential equations of a look (1)—(4).