Global Solutions for the zero-energy Novikov-Veselov equation by inverse scattering

Michael Music, Peter Perry

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Using the inverse scattering method, we construct global solutions to the Novikov-Veselov equation for real-valued decaying initial data q0 with the property that the associated Schrödinger operator is nonnegative. Such initial data are either critical (an arbitrarily small perturbation of the potential makes the operator nonpositive) or subcritical (sufficiently small perturbations of the potential preserve non-negativity of the operator). Previously, Lassas, Mueller, Siltanen and Stahel proved global existence for critical potentials, also called potentials of conductivity type. We extend their results to include the much larger class of subcritical potentials. We show that the subcritical potentials form an open set and that the critical potentials form the nowhere dense boundary of this open set. Our analysis draws on previous work of the first author and on ideas of Grinevich and Manakov.

Original languageEnglish
Article number3413
Issue number7
StatePublished - Jun 6 2018

Bibliographical note

Publisher Copyright:
© 2018 IOP Publishing Ltd & London Mathematical Society.


  • Novikov-Veselov equation
  • dbar-methods
  • inverse scattering

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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