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.

中文翻译：

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关于管理四阶Schrödinger-Hartree方程

我们考虑与色散系数可变的四阶非线性Schrödinger-Hartree方程相关的柯西问题。可变色散系数在时间函数中假定为连续或周期性且分段恒定。我们证明了$ H ^ s $空间中初始数据的局部和全局适定性结果。我们还分析了快速色散管理的规模极限，并分析了平均色散模型的收敛性。