N-Soliton Solutions and Inelastic Interaction For a Discretized Second-Order in Time Nonlinear Schrödinger Equation

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.