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arXiv · 2305.13531

Threshold dynamics for the 3$d$ radial NLS with combined nonlinearity

Alex H. Ardila·Jason Murphy·Jiqiang Zheng
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Abstract

We consider the nonlinear Schr\"odinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: \[ (i\partial_t+\Delta)u = |u|^2 u - |u|^4 u. \] In [18, 23], 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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Alex H. Ardila, Jason Murphy, Jiqiang Zheng. 2023-05-22. Threshold dynamics for the 3$d$ radial NLS with combined nonlinearity. https://arxiv.org/abs/2305.13531

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