Advances in Differential Equations

Stability of stationary waves for a quasilinear Schrödinger equation in space dimension 2

Mathieu Colin

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Abstract

In this paper, we study the existence and the properties of standing waves of the form $u_{\omega}(x,t)=\phi_{\omega}(x)e^{i\omega t},$ where $ x\in \mathbb R^2,$ $t\geq 0$, for a quasilinear Schrödinger equation. Using the minimization method introduced by T. Cazenave and P.L. Lions, we prove a stability theorem for such waves.

Article information

Source
Adv. Differential Equations, Volume 8, Number 1 (2003), 1-28.

Dates
First available in Project Euclid: 19 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355926866

Mathematical Reviews number (MathSciNet)
MR1946556

Zentralblatt MATH identifier
1042.35074

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35A15: Variational methods 35B35: Stability

Citation

Colin, Mathieu. Stability of stationary waves for a quasilinear Schrödinger equation in space dimension 2. Adv. Differential Equations 8 (2003), no. 1, 1--28. https://projecteuclid.org/euclid.ade/1355926866


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