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2014 Miura maps and inverse scattering for the Novikov–Veselov equation
Peter Perry
Anal. PDE 7(2): 311-343 (2014). DOI: 10.2140/apde.2014.7.311


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.


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Peter Perry. "Miura maps and inverse scattering for the Novikov–Veselov equation." Anal. PDE 7 (2) 311 - 343, 2014.


Received: 9 November 2012; Revised: 18 December 2013; Accepted: 10 February 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 06322734
MathSciNet: MR3218811
Digital Object Identifier: 10.2140/apde.2014.7.311

Primary: 37K15
Secondary: 35Q53 , 47A40 , 78A46

Keywords: Davey–Stewartson equation , Miura map , Novikov–Veselov equation

Rights: Copyright © 2014 Mathematical Sciences Publishers


Vol.7 • No. 2 • 2014
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