Traveling waves for the cubic Szegő equation on the real line

Oana Pocovnicu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)379-404
Number of pages26
JournalAnalysis and PDE
Issue number3
Publication statusPublished - 2011


  • nonlinear Schrodinger equations
  • Szego equation
  • integrable Hamiltonian systems
  • Lax pair
  • traveling wave
  • orbital stability
  • Hankel operators


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