Geodesic
$2+1$ Toda chain. I. Inverse scattering method
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 3, pp. 323-339 Cet article a éte moissonné depuis la source Math-Net.Ru

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A formal scheme of the inverse scattering method is constructed for the $2+1$ Toda chain in the class of rapidly decreasing Cauchy data. 
@article{TMF_1988_75_3_a0,
     author = {V. D. Lipovskii and A. V. Shirokov},
     title = {$2+1${~Toda} chain. {I.~Inverse} scattering method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--339},
     year = {1988},
     volume = {75},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_3_a0/}
}
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V. D. Lipovskii; A. V. Shirokov. $2+1$ Toda chain. I. Inverse scattering method. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 3, pp. 323-339. http://geodesic.mathdoc.fr/item/TMF_1988_75_3_a0/

[1] Mikhailov A. V., Pisma v ZhETF, 39:7 (1979), 443–448

[2] Mikhailov A. V., Physica D, 3:1–2 (1981), 73–117 | DOI | Zbl

[3] Mikhailov A. V., Olshanetsky M. A., Perelomov A. M., Commun. Math. Phys., 79:4 (1981), 473–488 | DOI | MR

[4] Leznov A. N., Saveliev M. A., Lett. Math. Phys., 3:5 (1979), 489–494 | DOI | MR | Zbl

[5] Matveev V. B., Lett. Math. Phys., 3 (1979), 217–222 | DOI | MR | Zbl

[6] Matveev V. B., Sall M. A., Zap. nauchn. semin. LOMI, 101, 1981, 111–118 | MR

[7] Sall M. A., TMF, 53:2 (1982), 227–237 | MR | Zbl

[8] Babich M. V., Matveev V. B., Sall M. A., Zap. nauchn. semin. LOMI, 145, 1985, 34–45 | MR | Zbl

[9] Takhtadzhyan L. A., Faddeev L. D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[10] Faddeev L. D., Sovremennye problemy matematiki, 3, VINITI, M., 1974, 93–180 | MR

[11] Zakharov V. E., Manakov S. V., Sov. Sci. Rev., 1 (1979), 133–190

[12] Manakov S. V., Physica D, 3:1 (1981), 420–427 | DOI | Zbl

[13] Fokas A. S., Ablowitz M. J., Stud. Appl. Math., 69 (1983), 211–228 | DOI | MR | Zbl

[14] Ablowitz M. J., Bar Iaakov D., Fokas A. S., Stud. Appl. Math., 62 (1983), 135–143 | DOI | MR

[15] Khermander L., Vvedenie v teoriyu funktsii neskolkikh kompleksnykh peremennykh, Mir, M., 1968 | MR

[16] Rudin U., Teoriya funktsii v edinichnom share iz $\mathbb{C}^n$, Mir, M., 1984 | MR | Zbl

[17] Beals R., Coifman R., Séminaire Goulaoric–Meyer–Shwartz, no. 22, Ecole Polytechnique, Palaiseau, 1980–81 | MR

[18] Nachman A. J., Ablowitz M. J., Stud. Appl. Math., 71:3 (1984), 243–250 | DOI | MR | Zbl

[19] Zakharov V. E., Manakov S. V., Zap. nauchn. semin. LOMI, 133, 1984, 77–91 | MR | Zbl

[20] Zakharov V. E., Manakov S. V., Funkts. analiz i ego prilozh., 19:2 (1985), 11–25 | MR

[21] Fokas A. S., Ablowitz M. J., J. Math. Phys., 25:8 (1984), 2494–2505 | DOI | MR | Zbl

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

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

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

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

[26] Ragnisko O., Santini M., Chitlaru Briggs S., Ablowitz M. J., An example of $\partial$-problem arising in a finite difference context: direct and inverse problem for discrete analogue of the equation $\psi_{xx}+u\psi=\mathrm{\sigma}\psi_y$, Preprint No 488, Universitá di Roma La Sapienza, Roma, 1985 | MR

[27] Lipovskii V. D., DAN SSSR, 286:2 (1986), 334–338 | MR

[28] Arkadev V. A., Pogrebkov A. K., Polivanov M. K., Zap. nauchn. semin. LOMI, 133, 1984, 17–37 | MR | Zbl

[29] Pogrebkov A. K., Polivanov M. K., Sov. Sci. Rev. Ser. C. Rev. Math. Phys., 5 (1985), 120–169 | MR

[30] Manakov S. V., Zakharov V. E., Lett. Math. Phys., 5:3 (1981), 247–253 | DOI | MR