Abstract: In[2] from the study of the nonlinear Langmuir wave of plasma,a class of nonlinear Schrödinger equations with integral terms is presented for the perturbation of Zakhrov equation with soliton solution.In this paper, based on[1] we consider the more general initial problem of the fol-lowing two classes of the nonlinear Schrödinger system of equations with the integral pairing method.