$H^2$-scattering for systems of weakly coupled fourth-order NLS equations in low space dimensions

TL;DR

This paper establishes large-data scattering and wave operator existence for systems of weakly coupled fourth-order nonlinear Schrödinger equations in low dimensions, introducing new Morawetz identities to analyze solution decay.

Contribution

It provides the first large-data scattering results for such systems in low dimensions and develops novel Morawetz estimates for decay analysis.

Findings

Proved large-data scattering in energy space.

Established existence of wave operators.

Developed new Morawetz identities for decay estimates.

Abstract

We prove large-data scattering and existence of wave operators in the energy space for the systems of $N$ defocusing fourth-order Schr\"odinger equations with mass-supercritical and energy-subcritical power-type nonlinearity. In addition, new nonlinear interaction Morawetz identities and inequalities are given, suitable to shed lights on the decay of the solution with respect some Lebesgue norms when the space dimensions are $d=3,4$.