Geodesic
Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 408-416 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We demonstrate how the Moutard transformation of two-dimensional Schrödinger operators acts on the Faddeev eigenfunctions on the zero-energy level and present some explicitly computed examples of such eigenfunctions for smooth rapidly decaying potentials of operators with a nontrivial kernel and for deformed potentials corresponding to blowup solutions of the Novikov–Veselov equation.
Keywords: Schrödinger operator, Faddeev eigenfunction, scattering data.
Mots-clés : Moutard transformation 
@article{TMF_2013_176_3_a5,
     author = {I. A. Taimanov and S. P. Tsarev},
     title = {Faddeev eigenfunctions for two-dimensional {Schr\"odinger} operators via {the~Moutard} transformation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {408--416},
     year = {2013},
     volume = {176},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a5/}
}
TY  - JOUR
AU  - I. A. Taimanov
AU  - S. P. Tsarev
TI  - Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 408
EP  - 416
VL  - 176
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a5/
LA  - ru
ID  - TMF_2013_176_3_a5
ER  - 
%0 Journal Article
%A I. A. Taimanov
%A S. P. Tsarev
%T Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 408-416
%V 176
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a5/
%G ru
%F TMF_2013_176_3_a5
I. A. Taimanov; S. P. Tsarev. Faddeev eigenfunctions for two-dimensional Schrödinger operators via the Moutard transformation. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 408-416. http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a5/

[1] I. A. Taimanov, S. P. Tsarev, TMF, 157:2 (2008), 188–207 | DOI | DOI | MR | Zbl

[2] L. D. Faddeev, Dokl. AN SSSR, 165:3 (1965), 514–517 | Zbl

[3] L. D. Faddeev, “Obratnaya zadacha kvantovoi teorii rasseyaniya. II”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 3, VINITI, M., 1974, 93–180 | DOI | MR | Zbl

[4] R. G. Novikov, G. M. Khenkin, UMN, 42:3(255) (1987), 93–152 | DOI | MR | Zbl

[5] P. G. Grinevich, R. G. Novikov, Phys. Lett. A, 376:12–13 (2012), 1102–1106, arXiv: 1110.3157 | DOI | MR | Zbl

[6] P. G. Grinevich, R. G. Novikov, Faddeev eigenfunctions for multipoint potentials, arXiv: 1211.0292

[7] P. G. Grinevich, TMF, 69:2 (1986), 307–310 | DOI | MR | Zbl

[8] P. G. Grinevich, S. P. Novikov, Funkts. analiz i ego pril., 22:1 (1988), 23–33 | DOI | MR | Zbl

[9] I. N. Vekua, Obobschennye analiticheskie funktsii, Nauka, M., 1959 | MR | MR | Zbl

[10] R. G. Novikov, J. Funct. Anal., 103:2 (1992), 409–463 | DOI | MR | Zbl

[11] M. Boiti, J. J. P. Leon, M. Manna, F. Pempinelli, Inverse Problems, 3:1 (1987), 25–36 | DOI | MR | Zbl

[12] H.-C. Hu, S.–Y. Lou, Q.-P. Liu, Chinese Phys. Lett., 20:9 (2003), 1413–1415 | DOI | MR

[13] A. P. Veselov, S. P. Novikov, Dokl. AN SSSR, 279:1 (1984), 20–24 | MR | Zbl

[14] P. A. Perry, Miura maps and inverse scattering for the Novikov–Veselov equation, arXiv: 1201.2385 | MR

[15] M. Music, P. A. Perry, S. Siltanen, Exceptional circles of radial potentials, arXiv: 1211.3520 | MR