Geodesic
The inverse scattering method in a form invariant with respect to representations of the internal symmetry algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 156-160 
A. N. Leznov. The inverse scattering method in a form invariant with respect to representations of the internal symmetry algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 1, pp. 156-160. http://geodesic.mathdoc.fr/item/TMF_1984_58_1_a12/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the example of the sine–Gordon equation, a method is developed for finding soliton solutions that does not involve a specific matrix realization of the Lax L–A pair but uses directly the properties of the internal symmetry algebra of the corresponding equations.

[1] Kruskal M. D., Lecture Notes in Phys., 38, 1975, 310–354 ; Zakharov V. E., Lecture Notes in Math., Springer-Verlag, Berlin, 1978; Drinfeld V. G., Krichever M., Manin Yu. I., Novikov S. P., Sov. Science Rev.- Phys. Rev., 1978; Захаров В. Е., Манаков С. В., Новиков С. П., Питаевский Л. П., Теория солитонов: Метод обратной задачи рассеяния, Наука, М., 1980 ; Захаров В. Е., Шабат А. Б., Функ. анализ и его прилож., 8:3 (1974), 43–53 ; Лакс П., Математика, 13:5 (1969), 128–150; Фаддеев Л. Д., Соврем. проблемы матем., 3, 1974, 93–180 | DOI | MR | Zbl | MR | Zbl | MR | Zbl | MR | Zbl

[2] Zhiber A. V., Shabat A. B., DAN SSSR, 247:5 (1979), 1103–1107 ; Жибер А. В., Ибрагимов Н. Х., Шабат А. Б., ДАН СССР, 249:1 (1979), 26–29 ; Ибрагимов А. В., Шабат А. Б., ДАН СССР, 244:1 (1979), 56–61 ; Функц. анализ и его прилож., 14:1 (1980), 25–36 | MR | MR | Zbl | MR | MR | Zbl

[3] Leznov A. N., Smirnov V. G., Shabat A. B., TMF, 51:1 (1982), 10–21 | MR | Zbl

[4] Kats V. G., Izv. AN SSSR, ser. matem., 32 (1968), 1323–1367 | MR | Zbl

[5] Leznov A. N., Smirnov V. G., Lett. Math. Phys., 5 (1981), 31–36 | DOI | MR | Zbl

[6] Bogolyubov N. N., Izb. trudy, t. 2, Naukova dumka, Kiev, 1970 | MR

[7] Zakharov V. E., Takhtadzhyan L. A., Faddeev L. D., DAN SSSR, 219:6 (1974), 1334–1337 | MR | Zbl