Results on solutions of several systems of the product type complex partial differential difference equations

This article is devoted to exploring the solutions of several systems of the first-order partial differential difference equations (PDDEs) with product type {u(z+c[alpha(1)u(z)+beta(1)u(z1) + gamma(1)u(z2) + alpha(2)v(z) + beta(2)v(z1) + gamma(2)v(z2)] = 1, v(z+c)[alpha(1)v(z)+beta(1)v(z1) + gamma(1)v(z2) + alpha(2)u(z) + beta(2)u(z1) + gamma(2)u(z2)] = 1, where c=(c(1),c(2)) is an element of C-2 , alpha(j), beta(j), gamma(j) is an element of C, j = 1, 2. Our theorems about the forms of the transcendental solutions for these systems of PDDEs are some improvements and generalization of the previous results given by Xu, Cao and Liu. Moreover, we give some examples to explain that the forms of solutions of our theorems are precise to some extent.