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

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