We review recent progress in theory and computation for the Novikov-Veselov (NV) equation with potentials decaying at infinity, focusing mainly on the zero-energy case. The inverse scattering method for the zeroenergy 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.
|Title of host publication||Contemporary Mathematics|
|Number of pages||46|
|State||Published - 2015|
Bibliographical notePublisher Copyright:
© 2015 American Mathematical Society.
ASJC Scopus subject areas
- Mathematics (all)