Miura maps and inverse scattering for the Novikov-Veselov equation

DOI10.2140/apde.2014.7.311zbMath1405.37081arXiv1201.2385OpenAlexW1993108676MaRDI QIDQ2509679

Peter A. Perry

Publication date: 29 July 2014

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.2385

zbMATH Keywords

Novikov-Veselov equationDavey-Stewartson equationmiura map

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory of linear operators (47A40) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items (10)

Low Regularity Local Well-Posedness for the Zero Energy Novikov–Veselov Equation ⋮ Global Solutions for the zero-energy Novikov–Veselov equation by inverse scattering ⋮ Two kinds of important bifurcation phenomena of nonlinear waves in a generalized Novikov-Veselov equation ⋮ Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation ⋮ The Novikov-Veselov equation and the inverse scattering method. I: Analysis ⋮ Faddeev eigenfunctions for two-dimensional Schrödinger operators via the moutard transformation ⋮ Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II. ⋮ Numerical study of blow-up and stability of line solitons for the Novikov–Veselov equation ⋮ The nonlinear Fourier transform for two-dimensional subcritical potentials ⋮ Well-posedness and ill-posedness results for the Novikov-Veselov equation

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