The inverse scattering transform for the defocusing \(N(N>3)\) -component nonlinear Schrödinger equation with nonzero boundary conditions still remains open. In this paper, we investigate the inverse scattering analysis of the defocusing \(N(N\geqslant 2)\) -component nonlinear Schrödinger equation with a special class of nonzero boundary conditions. Through two modified Lax pairs, the direct problem is shown to be well posed for a class of initial values. By introducing the tensor product and the generalized cross product, a complete set of analytic eigenfunctions and their symmetries are established for characterizing the inverse problem. It has been shown that the solution of the defocusing N-component nonlinear Schrödinger equation can be expressed in terms of the solution of a \(3\times 3\) block matrix Riemann–Hilbert problem. In the reflectionless case, some soliton and breather solutions are obtained with graphical descriptions.
