The study of solutions of several systems of the product type nonlinear partial differential difference equations

: The purpose of this article is to investigate the solutions of several systems of the nonlinear partial differential difference equations (PDDEs) (including second order partial differential, mixed partial differential and complex difference) and ({l f (z z + c )( g z 1 + g z 1 z 1 ) = 1, g ( z + c )( f z 1 +fz1z1) f z 1 z 1 ) = 1, ({l f (z z + c )( g z 1 + g z 1 z 2 ) = 1, g ( z + c )( f z 1 +fz1z2) f z 1 z 2 ) = 1, ({lf (z z + c )( f z 1 + g z 1 z 2 ) = 1, g ( z + c )( g z 1 + f z 1 z 2 ) = 1, where c = (c1, c 1 , c 2 ) E (C2. 2 . We establish some theorems concerning the forms of the pair of solutions for these systems of PDDEs which are some improvements and generalization of the previous results given by Gao, Liu and Xu. Moreover, some examples show that the forms of solutions of our theorems are precise to some extent.