On the management fourth-order Schrödinger-Hartree equation

2019/05/20 by Banquet, Carlos, Villamizar-Roa, Élder J. · 1 citation
#35A01 #35B40 #35G25 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.08159

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 fast dispersion management and the convergence to a model with averaged dispersions.

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• Existence and asymptotical behavior of normalized solutions to focusing biharmonic HLS upper critical Hartree equation with a local perturbation

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