Tohoku Mathematical Journal

Stability of a stationary solution for the Lugiato-Lefever equation

Tomoyuki Miyaji, Isamu Ohnishi, and Yoshi Tsutsumi

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We study the stability of a stationary solution for the Lugiato-Lefever equation with the periodic boundary condition in one space dimension, which is a damped and driven nonlinear Schrödinger equation introduced to model the optical cavity. In this paper, we prove the Strichartz estimates for the linear damped Schrödinger equation with potential and external forcing and investigate the stability of certain stationary solutions under the initial perturbation within the framework of $L^2$.

Article information

Tohoku Math. J. (2), Volume 63, Number 4 (2011), 651-663.

First available in Project Euclid: 6 January 2012

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Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B35: Stability


Miyaji, Tomoyuki; Ohnishi, Isamu; Tsutsumi, Yoshi. Stability of a stationary solution for the Lugiato-Lefever equation. Tohoku Math. J. (2) 63 (2011), no. 4, 651--663. doi:10.2748/tmj/1325886285.

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