Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation

In this work, we study at the L 2 – level global well-posedness as well as long-time stability of an initial-boundary value problem, posed on a bounded interval, for a generalized higher order nonlinear Schrodinger equation, modeling the propagation of pulses in optical fiber, with a localized damping term. In addition, we implement a precise and efficient code to study the energy decay of the higher order nonlinear Schrodinger equation and we prove its convergence and exponential stability of the discrete energy.