Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation. (15th August 2021)

• Record Type: Journal Article
• Authors: Cavalcanti, Marcelo M.; Corrêa, Wellington J.; Faminskii, Andrei V.; Sepúlveda C., Mauricio A.; Véjar-Asem, Rodrigo
• Is Part Of: Computers & mathematics with applications. Volume 96(2021)
• Page Start: 188
• Page End: 208
• Publication Date: 2021-08-15
• Subjects: Higher order Schrödinger equation -- Localized dissipation -- Finite differences -- Asymptotic behavior; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.05.001
• Languages: English
• ISSNs: 0898-1221

Abstract

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.