Abstract
Nonlinear Schrödinger (NLS)-type equations can describe some physical phenomena in nonlinear optics , fluids, plasmas, etc. Under consideration in this paper is a discretized second-order in time nonlinear Schrödinger equation . Conservation laws and N -fold Darboux transformation (DT) are constructed by means of symbolic computations and its Lax representation. N -soliton solutions in terms of determinant are derived with the obtained DT. Structures of these solutions are shown graphically. Inelastic interaction phenomena between/among the two-, three-and four-soliton solutions are discussed, they might be helpful for understanding some physical phenomena.
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