具有三波相互作用的非线性薛定谔系统的奇异扰动问题

Yuki Osada
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引用次数: 0

摘要

在本文中,我们考虑了以下具有三波相互作用的非线性薛定谔系统的基态尖峰位置(\(\varepsilon \rightarrow +0\)。此外,我们还研究了决定尖峰位置的一个量 \(\inf _{x \in {\mathbb {R}}^N} {\tilde{c}}({{textbf{V}}}(x);\gamma )\) 的渐近行为。特别是,我们给出了在\(\gamma\)足够大和足够小的情况下,(\({\mathcal {P}}_\varepsilon \))的基态的尖锐渐近行为。此外,我们还考虑了(\({\mathcal {P}}_\varepsilon \))的所有基态都是标量或矢量时的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A singular perturbation problem for a nonlinear Schrödinger system with three wave interaction

A singular perturbation problem for a nonlinear Schrödinger system with three wave interaction

In this paper, we consider the locations of spikes of ground states for the following nonlinear Schrödinger system with three wave interaction

as \(\varepsilon \rightarrow +0\). In addition, we study the asymptotic behavior of a quantity \(\inf _{x \in {\mathbb {R}}^N} {\tilde{c}}({{\textbf{V}}}(x);\gamma )\) as \(\gamma \rightarrow \infty \) which determines locations of spikes. In particular, we give the sharp asymptotic behavior of a ground states of (\({{\mathcal {P}}}_\varepsilon \)) for \(\gamma \) sufficiently large and small, respectively. Furthermore, we consider when all the ground states of (\({{\mathcal {P}}}_\varepsilon \)) are scalar or vector.

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