Strong instability of standing waves for nonlinear Schr\"{o}dinger equations with a partial confinement

Masahito Ohta

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arXiv · 1706.02100

Strong instability of standing waves for nonlinear Schr\"{o}dinger equations with a partial confinement

Masahito Ohta

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Abstract

We study the instability of standing wave solutions for nonlinear Schr\"{o}dinger equations with a one-dimensional harmonic potential in dimension $N\ge 2$. We prove that if the nonlinearity is $L^2$-critical or supercritical in dimension $N-1$, then any ground states are strongly unstable by blowup.

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Masahito Ohta. 2017-06-07. Strong instability of standing waves for nonlinear Schr\"{o}dinger equations with a partial confinement. https://arxiv.org/abs/1706.02100

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