Stability And Solitons For A Parity-time-symmetric Vector Nonlinear Schr(?)dinger System

In recent years,the PT symmetric system is a new type of optical structure,which has great applications in the fields of communication and physics.In this paper,we consider the two-coupled nonlinear Schr(?)dinger equations with parity-time-symmetric potential in the presence of four-wave mixing.First of all,we use the linear transformation to obtain the solitary wave solutions of the Schr(?)dinger equation with the independent nonlinear Schr(?)dinger equation.Secondly,We construct the soliton solutions for the vector nonlinear Schr(?)dinger equations with PT-symmetric k-wave-number Scarff-? potential and PT-symmetric multiwell Scarff-? potential.Then the linear-stability spectrum for solitary waves is studied.Moreover,soliton solutions in high dimensional case are also considered.