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@article{MT_2021_24_2_a10, author = {U. A. Hoitmetov}, title = {Integrating the loaded {KdV} equation with a~self-consistent source of integral type in the class of rapidly decreasing complex-valued functions}, journal = {Matemati\v{c}eskie trudy}, pages = {181--198}, publisher = {mathdoc}, volume = {24}, number = {2}, year = {2021}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MT_2021_24_2_a10/} }
TY - JOUR AU - U. A. Hoitmetov TI - Integrating the loaded KdV equation with a~self-consistent source of integral type in the class of rapidly decreasing complex-valued functions JO - Matematičeskie trudy PY - 2021 SP - 181 EP - 198 VL - 24 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MT_2021_24_2_a10/ LA - ru ID - MT_2021_24_2_a10 ER -
%0 Journal Article %A U. A. Hoitmetov %T Integrating the loaded KdV equation with a~self-consistent source of integral type in the class of rapidly decreasing complex-valued functions %J Matematičeskie trudy %D 2021 %P 181-198 %V 24 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/MT_2021_24_2_a10/ %G ru %F MT_2021_24_2_a10
U. A. Hoitmetov. Integrating the loaded KdV equation with a~self-consistent source of integral type in the class of rapidly decreasing complex-valued functions. Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 181-198. http://geodesic.mathdoc.fr/item/MT_2021_24_2_a10/
[1] Blaschak V. A., “Analog obratnoi zadachi teorii rasseyaniya dlya nesamosopryazhennogo operatora. I”, Differents. uravneniya, 4:8 (1968), 1519–1533
[2] Blaschak V. A., “Analog obratnoi zadachi teorii rasseyaniya dlya nesamosopryazhennogo operatora. II”, Differents. uravneniya, 4:10 (1968), 1915–1924
[3] Zamonov M. Z., Khasanov A. B., Khoitmetov U. A., “Integrirovanie uravneniya KdF s samosoglasovannym istochnikom integralnogo tipa v klasse bystroubyvayuschikh kompleksnoznachnykh funktsii”, Izv. AN RTadzh. Otd. Fiz-mat., khim. i geol. nauk, 2007, no. 4(129), 7–21
[4] Kozhanov A. I., “Nelineinye nagruzhennye uravneniya i obratnye zadachi”, Zh. vychisl. matem. i matem. fiz., 44:4 (2004), 694–716 | Zbl
[5] Levitan B. M., Obratnye zadachi Shturma — Liuvillya, Nauka, M., 1984
[6] Marchenko V. A., Operatory Shturma — Liuvillya i ikh prilozheniya, Naukova dumka, Kiev, 1977
[7] Nakhushev A. M., “Nagruzhennye uravneniya i ikh prilozheniya”, Differents. uravneniya, 19:1 (1983), 86–94 | Zbl
[8] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995
[9] Faddeev L. D., “Svoistva $S$-matritsy odnomernogo uravneniya Shredingera”, Tr. Mat. in-ta im. V. A. Steklova, 73, 1964, 314–336 | Zbl
[10] Khasanov A. B., Khoitmetov U. A., “Ob integrirovanii uravneniya Kortevega-de Friza v klasse bystroubyvayuschikh kompleksnoznachnykh funktsii”, Izv. vuzov. Matem., 2018, no. 3, 79–90 | Zbl
[11] Khasanov A. B., Matyakubov M. M., “Integrirovanie nelineinogo uravneniya Kortevega-de Friza s dopolnitelnym chlenom”, TMF, 203:2 (2020), 192–204 | Zbl
[12] Khoitmetov U. A., “Integrirovanie obschego uravneniya KdF s samosoglasovannym istochnikom integralnogo tipa”, Dokl. AN RTadzh., 50:4 (2007), 307–311
[13] Yakhshimuratov A. B., Matëkubov M. M., “Integrirovanie nagruzhennogo uravneniya Kortevega-de Friza v klasse periodicheskikh funktsii”, Izv. vuzov. Matem., 2016, no. 2, 87–92 | Zbl
[14] Gardner C. S., Greene I. M., Kruskal M. D., Miura R. M., “Method for solving the Korteweg-de Vries equation”, Phys. Rev. Lett., 19 (1967), 1095–1097 | DOI
[15] Kneser A., “Belastete Integralgleichungen”, Rend. Circ. Mat. Palermo, 37 (1914), 169–197 | DOI | Zbl
[16] Lax P. D., “Integrals of nonlinear equations of evolution and solitary waves”, Comm. Pure Appl. Math., 21:5 (1968), 467–490 | DOI | Zbl
[17] Leon J., Latifi A., “Solution of an initial-boundary value problem for coupled nonlinear waves”, J. Phys. A, Math. Gen., 23:8 (1990), 1385–1403 | DOI | Zbl
[18] Lichtenstein L., Vorlesungen über einige Klassen nichtlinearer Integralgleichungen und Integro-Differentialgleichungen nebst Anwendungen, Springer, Berlin, 1931
[19] Mel'nikov V. K., “Exact solutions of the Korteweg-de Vries equation with a self-consistent source”, Phys. Lett. A, 128:9 (1988), 488–492 | DOI