Analysis & PDE
- Anal. PDE
- Volume 4, Number 3 (2011), 379-404.
Traveling waves for the cubic Szegő equation on the real line
We consider the cubic Szegő equation in the Hardy space on the upper half-plane, where is the Szegő projector. It was first introduced by Gérard and Grellier as a toy model for totally nondispersive evolution equations. We show that the only traveling waves are of the form , where with . Moreover, they are shown to be orbitally stable, in contrast to the situation on the unit disk where some traveling waves were shown to be unstable.
Anal. PDE, Volume 4, Number 3 (2011), 379-404.
Received: 19 January 2010
Revised: 28 April 2010
Accepted: 29 May 2010
First available in Project Euclid: 20 December 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35B15: Almost and pseudo-almost periodic solutions 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Pocovnicu, Oana. Traveling waves for the cubic Szegő equation on the real line. Anal. PDE 4 (2011), no. 3, 379--404. doi:10.2140/apde.2011.4.379. https://projecteuclid.org/euclid.apde/1513731146