Journal
ANALYSIS & PDE
Volume 4, Issue 3, Pages 379-404Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/apde.2011.4.379
Keywords
nonlinear Schrodinger equations; Szego equation; integrable Hamiltonian systems; Lax pair; traveling wave; orbital stability; Hankel operators
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We consider the cubic Szego equation i partial derivative tu = Pi(vertical bar u vertical bar(2) u) in the Hardy space L-+(2) (R) on the upper half-plane, where Pi is the Szego projector. It was first introduced by Gerard and Grellier as a toy model for totally nondispersive evolution equations. We show that the only traveling waves are of the form C/(x - p), where p epsilon C with Im p < 0. 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.
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