Geodesic
Rational solitons of the Veselov–Novikov equations are reflectionless two-dimensional potentials at fixed energy
Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 2, pp. 307-310 
P. G. Grinevich. Rational solitons of the Veselov–Novikov equations are reflectionless two-dimensional potentials at fixed energy. Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 2, pp. 307-310. http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a14/
@article{TMF_1986_69_2_a14,
     author = {P. G. Grinevich},
     title = {Rational solitons of the {Veselov{\textendash}Novikov} equations are reflectionless two-dimensional potentials at fixed energy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {307--310},
     year = {1986},
     volume = {69},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a14/}
}
TY  - JOUR
AU  - P. G. Grinevich
TI  - Rational solitons of the Veselov–Novikov equations are reflectionless two-dimensional potentials at fixed energy
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1986
SP  - 307
EP  - 310
VL  - 69
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a14/
LA  - ru
ID  - TMF_1986_69_2_a14
ER  - 
%0 Journal Article
%A P. G. Grinevich
%T Rational solitons of the Veselov–Novikov equations are reflectionless two-dimensional potentials at fixed energy
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1986
%P 307-310
%V 69
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a14/
%G ru
%F TMF_1986_69_2_a14

Voir la notice de l'article provenant de la source Math-Net.Ru

Explicit examples are constructed of two-dimensional rational potentials that decrease at infinity and are reflectionless for given energy. It is shown that these potentials correspond to soliton solutions of the (2+1)-dimensional nonlinear equations found by Veselov and Novikov.

[1] Shadan K., Sabate P., Obratnye zadachi v kvantovoi teorii rasseyaniya, Mir, M., 1980 | MR

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

[3] Grinevich P. G., Novikov R. G., Funkts. analiz i ego prilozh., 19:4 (1985), 32–42 | MR | Zbl

[4] Grinevich P. G., Novikov R. G., DAN SSSR, 286:1 (1986), 19–22 | MR | Zbl

[5] Grinevich P. G., Manakov S. V., Funkts. analiz i ego prilozh., 20:2 (1986), 14–24 | MR | Zbl

[6] Novikov R. G., TMF, 66:2 (1986), 234–240 | MR | Zbl

[7] Fokas A. S., Ablovitz M. J., Stud. in Applied Math., 69:3 (1983), 211–228 | DOI | MR | Zbl