Exact gray multi-soliton solutions for nonlinear Schrödinger equation with variable coefficients

In this paper, the generalized nonlinear Schrödinger equation with variable coefficients is studied. First, exact gray one-soliton solution in explicit form is obtained by using the complex amplitude ansatz method. Second, the multi-soliton solutions are constructed through suitable mapping and the explicit two-soliton solution is generated. These solutions are useful in studying the propagation characteristics and interaction of dark (gray) solitons in inhomogeneous fiber system or in soliton management system. Finally, the stabilities of these solutions are discussed numerically.