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

Author

Cavalcanti, Marcelo M., Corrêa, Wellington J., Faminskii, Andrei V., Sepúlveda C., Mauricio A., and Véjar-Asem, Rodrigo

Subjects
*NONLINEAR Schrodinger equation, *EXPONENTIAL stability, *LIGHT propagation, *SCHRODINGER equation, *OPTICAL fibers, *FEMTOSECOND pulses, *FINITE differences
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. [ABSTRACT FROM AUTHOR]

Published
2021
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