Ryan Croke, Jennifer L Mueller, Michael Music, Peter Perry, Samuli Siltanen, Andreas Stahel
Published 2013-12-19Version 1
Recent progress in the theory and computation for the Novikov-Veselov (NV) equation is reviewed with initial potentials decaying at infinity, focusing mainly on the zero-energy case. The inverse scattering method for the zero-energy NV equation is presented in the context of Manakov triples, treating initial data of conductivity type rigorously. Special closed-form solutions are presented, including multisolitons, ring solitons, and breathers. The computational inverse scattering method is used to study zero-energy exceptional points and the relationship between supercritical, critical, and subcritical potentials.
A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy
The Novikov-Veselov Equation and the Inverse Scattering Method, Part I: Analysis
Miura Maps and Inverse Scattering for the Novikov-Veselov Equation
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