English

The Novikov-Veselov Equation: Theory and Computation

Analysis of PDEs 2013-12-20 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1312.5427,
  title  = {The Novikov-Veselov Equation: Theory and Computation},
  author = {Ryan Croke and Jennifer L Mueller and Michael Music and Peter Perry and Samuli Siltanen and Andreas Stahel},
  journal= {arXiv preprint arXiv:1312.5427},
  year   = {2013}
}