Demonstration of Inverse Scattering Transform in G-L-M Formalismfor NLS Equation in Normal Dispersion with Non-vanishing Boundary

Using the integral representation of the Jostsolution, we deduce some conditions as the kernel function N(x, y,t) if the Jost solution satisfies the two Lax equations. Then weverify the multi-soliton solution of NLS equation withnon-vanishing boundary conditions if we prove that these conditionscan be demonstrated by the GLM equation, which determines the kernelfunction N(x,y,t) in according to the inverse scattering method.