Miura maps and inverse scattering for the Novikov-Veselov equation

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13 Scopus citations

Abstract

We use the inverse scattering method to solve the zero-energy Novikov-Veselov (NV) equation for initial data of conductivity type, solving a problem posed by Lassas, Mueller, Siltanen, and Stahel. We exploit Bogdanov's Miura-type map which transforms solutions of the modified Novikov-Veselov (mNV) equation into solutions of the NV equation. We show that the Cauchy data of conductivity type considered by Lassas, Mueller, Siltanen, and Stahel lie in the range of Bogdanov's Miura-type map, so that it suffices to study the mNV equation. We solve the mNV equation using the scattering transform associated to the defocussing Davey-Stewartson II equation.

Original languageEnglish
Pages (from-to)311-343
Number of pages33
JournalAnalysis and PDE
Volume7
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Davey-stewartson equation
  • Miura map
  • Novikov-Veselov equation

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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