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On the management fourth-order Schrödinger-Hartree equation

  • * Corresponding author: Élder J. Villamizar-Roa

    * Corresponding author: Élder J. Villamizar-Roa

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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  • 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.

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


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  • Figure 1.  Sketch of the dispersion functions

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