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 language | English |
|---|---|
| Pages (from-to) | 311-343 |
| Number of pages | 33 |
| Journal | Analysis and PDE |
| Volume | 7 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2014 |
Keywords
- Davey-stewartson equation
- Miura map
- Novikov-Veselov equation
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Applied Mathematics