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

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

doi:10.1016/j.camwa.2021.05.001

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

Marcelo M Cavalcanti, Wellington J Corrêa + Show 3 more

https://doi.org/10.1016/j.camwa.2021.05.001

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Journal: Computers and Mathematics with Applications	Publication Date: May 31, 2021
Citations: 4

Affiliation: Universidade Estadual de Maringá, Universidade Tecnológica Federal do Paraná, University of Concepción, Peoples' Friendship University of Russia

#Localized Damping Term #Pulses In Optical Fiber + Show 8 more

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Abstract

In this work, we study at the L2 – 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.

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