Integral representation of solution manifolds for over determined systems with one weak singular and two super singular lines

In this paper, a over determined system of second-order partial differential equations with one weak singular and two super singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one weak singular and two super singular line. Under the condition of compatibility, introducing a new function, we come to a over determined system of partial differential equations of the second order with one weak singular and two super singular line of a simpler form. The integral representation of the manifold of solutions of the redefined second-order partial differential system with one weak singular and two super singular line is found explicitly through three arbitrary constants, for which initial data problems( Cauchy type problems) can be posed.