Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation. (15th August 2021) - Cavalcanti, Marcelo M.; Corrêa, Wellington J.; Faminskii, Andrei V.; Sepúlveda C., Mauricio A.; Véjar-Asem, Rodrigo
Abstract: 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 Schrödinger 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 Schrödinger equation and we prove its convergence and exponential stability of the discrete energy.