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arXiv · 2308.06856

Decomposition of global solutions of bi-laplacian Nonautonomous Schr\"odinger equations

Avy Soffer·Jiayan Wu·Xiaoxu Wu·Ting Zhang
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Abstract

We study the bi-Laplacian Schr\"odinger equation with a general interaction term, which may be linear or nonlinear and is allowed to be time-dependent. We show that global solutions to such equations decompose asymptotically into a free wave and a weakly localized component in all space dimensions. Moreover, in dimensions $n \geq 9$, we prove that the weakly localized component is in fact spatially localized. The proof is based on a suitably adapted construction of the Free Channel Wave Operator, building on the method recently developed in~\cite{SW20221}.

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Avy Soffer, Jiayan Wu, Xiaoxu Wu, Ting Zhang. 2023-08-13. Decomposition of global solutions of bi-laplacian Nonautonomous Schr\"odinger equations. https://arxiv.org/abs/2308.06856

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