Examples of solution of the inverse scattering problem and the equations of the 
Novikov–Veselov hierarchy from the scattering data of point potentials

Agaltsov, Alexey; Novikov , R. G.

doi:10.1070/RM9867

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Examples of solution of the inverse scattering problem and the equations of the Novikov–Veselov hierarchy from the scattering data of point potentials

MPS-Authors

/persons/resource/persons240755

Agaltsov, Alexey
Max Planck Institute for Solar System Research, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Agaltsov, A., & Novikov, R. G. (2019). Examples of solution of the inverse scattering problem and the equations of the Novikov–Veselov hierarchy from the scattering data of point potentials. Russian Mathematical Surveys, 74(3), 373-386. doi:10.1070/RM9867.

Cite as: https://hdl.handle.net/21.11116/0000-0006-681F-4

Abstract

The inverse scattering problem is considered for the two- dimensional Schrödinger equation at fixed positive energy. The results include inverse scattering reconstructions from the simplest scattering amplitudes. In particular, a complete analytic solution is given of the phased and phaseless inverse scattering problems for single-point potentials of Bethe– Peierls– Fermi–Zeldovich– Berezin–Faddeev type. Numerical inverse scattering reconstructions from the simplest scattering amplitudes are then studied using the method of the Riemann–Hilbert– Manakov problem in soliton theory. Finally, these numerical inverse scattering results are used to construct corresponding numerical solutions of the non-linear equations of the Novikov–Veselov hierarchy at fixed positive energy.