On the management fourth-order Schrödinger-Hartree equation

Carlos Banquet; Élder J. Villamizar-Roa

doi:10.3934/eect.2020037

Article Contents

2020, Volume 9, Issue 3: 865-889. Doi: 10.3934/eect.2020037

This issue Previous Article Time-varying integro-differential inclusions with Clarke sub-differential and non-local initial conditions: existence and approximate controllability Next Article Nonlocal final value problem governed by semilinear anomalous diffusion equations

On the management fourth-order Schrödinger-Hartree equation

Carlos Banquet^1, and
Élder J. Villamizar-Roa^2, ,

1.
Universidad de Córdoba, Departamento de Matemáticas y Estadística, A.A. 354, Montería, Colombia
2.
Universidad Industrial de Santander, Escuela de Matemáticas, Bucaramanga, A.A. 678, Colombia

^* Corresponding author: Élder J. Villamizar-Roa
^* Corresponding author: Élder J. Villamizar-Roa

Received: April 30, 2019

Revised: September 30, 2019

Early access: March 2020

Published: September 2020

The second author has been supported by the the Vicerrectoría de Investigación y Extensión-UIS and Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación Francisco José de Caldas, contrato Colciencias FP 44842-157-2016

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Abstract

We consider the Cauchy problem associated to the fourth-order nonlinear Schrödinger-Hartree equation with variable dispersion coefficients. The variable dispersion coefficients are assumed to be continuous or periodic and piecewise constant in time functions. We prove local and global well-posedness results for initial data in $ H^s $-spaces. We also analyze the scaling limit of the fast dispersion management and the convergence to a model with averaged dispersions.

Keywords:

Dispersion management,
fourth-order nonlinear Schrödinger-Hartree equation.

Mathematics Subject Classification: Primary: 35Q55; 35A01; Secondary: 35B40; 35G25.

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Figure 1. Sketch of the dispersion functions

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