The novikov-veselov equation: Theory and computation

R. Croke; J. L. Mueller; M. Music; P. Perry; S. Siltanen; A. Stahel

doi:10.1090/conm/635/12718

The novikov-veselov equation: Theory and computation

R. Croke, J. L. Mueller, M. Music, P. Perry, S. Siltanen, A. Stahel

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

6 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Contemporary Mathematics
Pages	25-70
Number of pages	46
DOIs	https://doi.org/10.1090/conm/635/12718
State	Published - 2015

Publication series

Name	Contemporary Mathematics
Volume	635
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Bibliographical note

Publisher Copyright:
© 2015 American Mathematical Society.

ASJC Scopus subject areas

General Mathematics

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10.1090/conm/635/12718

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AU - Perry, P.

AU - Siltanen, S.

AU - Stahel, A.

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AB - 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.

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The novikov-veselov equation: Theory and computation

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