THE THEORY OF NONLINEAR OVERDETERMINED SYSTEMS OF THREE AND FOUR DIFFERENTIAL EQUATIONS IN PRIVATE DERIVATIVES OF THE FIRST ORDER IN SPACE
This paper deals with the solution of nonlinear overridden systems of three and four first order partial differential equations in space. The author notes that the solutions of such systems of equations depend on the identical fulfillment of a number of conditions. For example, under identical fulfillment of four conditions of the solution variety of the system U x , U y = h i x,y,z;U, V x , i=1,2, U z = h 3 x,y,z;U, V, V x , contains three arbitrary constants. But in case of if these conditions are not satisfied identically, then the diversity of solutions of this system contains two arbitrary constants.