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Article Contents

# Instability of bound states for 2D nonlinear Schrödinger equations

• We study standing wave solutions of the form $e^{i(\omega t+m\theta)}\phi(r)$ to nonlinear Schrödinger equation

$iu_t+\Delta u+|u|^{p-1}u=0\quad$ for $x\in \mathbb R^2$

and $t>0$, where $(r,\theta)$ are polar coordinates and $m\in\mathbb N$. Using the Evans function, we prove linear instability of standing wave solutions with nodes in the case where $p>3$.

Mathematics Subject Classification: 35B35, 35Q55, 35J60, 35B05.

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