结合非线性的三维径向NLS的阈值动力学

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-09-29 DOI:10.1016/j.jde.2025.113800

Alex H. Ardila , Jason Murphy , Jiqiang Zheng

引用次数: 0

摘要

我们考虑三维空间中具有聚焦五次和散焦三次非线性的非线性Schrödinger方程：（i∂t+Δ）u=|u|2u−|u|4u。在[18]中，作者对能量约束E(u)<Ec(W)下解的动力学进行了分类，其中W为五次NLS基态，Ec为五次NLS能量。在这项工作中，我们在阈值E(u)=Ec(W)处对H1解的动力学进行分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Threshold dynamics for the 3d radial NLS with combined nonlinearity

We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions:

(i \partial_{t} + Δ) u = | u |^{2} u - | u |^{4} u .

In [18], the authors classified the dynamics of solutions under the energy constraint

E (u) < E^{c} (W)

, where W is the quintic NLS ground state and

E^{c}

is the quintic NLS energy. In this work we classify the dynamics of

H^{1}

solutions at the threshold

E (u) = E^{c} (W)

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics