Instability of bound states for 2D nonlinear Schrödinger equations

Tetsu Mizumachi

doi:10.3934/dcds.2005.13.413

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2005, Volume 13, Issue 2: 413-428. Doi: 10.3934/dcds.2005.13.413

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Instability of bound states for 2D nonlinear Schrödinger equations

Tetsu Mizumachi^1,

1.
Department of Mathematical Sciences, Yokohama City University, Seto 22-2, 236-0027

Received: May 31, 2004

Revised: October 31, 2004

Published: January 2005

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Abstract

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 $p>3$.

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

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