Generalized partial derivative-dressing method for coupled nonlocal NLS equation

In this paper, we investigate a general integrable coupled nonlocal nonlinear Schrodinger(cnNLS)equation with reverse space and reverse time. First, we introduce a 4-component nonlocal nonlinear Schrodinger (nNLS) equation. Based on two 3x3 matrices partial derivative-problems, we obtain the N-soliton solutions of the 4-component nNLS equation by constructing two spectral transformation matrices R and Rwith some specific scattering data{ ki,alpha i,beta i}(i-1)(N) and {lambda j, xi j, eta j}(j=1)((N) over bar). We have the symmetry condition for R and R. We express the determinant in the N-soliton solution in the form of sums with the help of Cauchy matrix properties to facilitate follow-up reduction. The general nonlocal reductio nof the 4-component nNLS equation to the cnNLS equation is discussed in detail. After obtaining the1-soliton solution of cnNLS equation, we analyse the nonsingular region of the single soliton solution ,with spectral parametersk 1 and lambda 1 are conjugate. We also draw some typical images of 1-solitonsolution. The 2-soliton solutions for cnNLS equation are derived and their asymptotic behaviours are discussed. After that we discuss the dynamic behaviour of the two waves in 2-soliton solution under the condition of different spectral parameters values.