Instability of bound states for 2D nonlinear Schrödinger equations

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February 2005, 13(2): 413-428. doi: 10.3934/dcds.2005.13.413

Instability of bound states for 2D nonlinear Schrödinger equations

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

Received June 2004 Revised November 2004 Published April 2005

Abstract
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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 $p>3$.

Keywords: standing wave solutions., instability, Nonlinear Schrödinger equation.

Mathematics Subject Classification: 35B35, 35Q55, 35J60, 35B0.

Citation: Tetsu Mizumachi. Instability of bound states for 2D nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 413-428. doi: 10.3934/dcds.2005.13.413

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