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

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. © 2021 Elsevier Ltd

Authors
Cavalcanti M.M.1 , Corrêa W.J.2 , Faminskii A.V. 3 , Sepúlveda C.M.A. , Véjar-Asem R.4
Journal
Computers and Mathematics with Applications
Publisher
Elsevier Ltd
Language
English
Pages
188-208
Status
Published
Link
External link
DOI
10.1016/j.camwa.2021.05.001
Volume
96
Year
2021
Organizations
  • 1 Department of Mathematics, State University of Maringá, Maringá, PR 87020-900, Brazil
  • 2 Academic Department of Mathematics, Federal Technological University of Paraná, Campuses Campo Mourão, Campo Mourão, PR 87301-899, Brazil
  • 3 Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
  • 4 Departamento de Ingeniería Matemática, Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción, Casilla 160-C, Concepción, Chile
Keywords
Asymptotic behavior; Finite differences; Higher order Schrödinger equation; Localized dissipation
Date of creation
20.07.2021
Date of change
15.11.2021
Short link
https://repository.rudn.ru/en/records/article/record/74158/
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