On the~sine-Gordon equation with a~self-consistent source
Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 153-166.

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We use the method of the inverse scattering problem to solve the sine-Gordon equation with a self-consistent source which corresponds to moving eigenvalues of the corresponding spectral problem.
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A. B. Khasanov; G. U. Urazboev. On the~sine-Gordon equation with a~self-consistent source. Matematičeskie trudy, Tome 11 (2008) no. 1, pp. 153-166. http://geodesic.mathdoc.fr/item/MT_2008_11_1_a7/

[1] Ablovits M., Sigur Kh., Solitony i metod obratnoi zadachi, Mir, M., 1987 | MR

[2] Gasymov M. G., Levitan B. M., “Opredelenie sistemy Diraka po faze rasseyaniya”, Dokl. AN SSSR, 167:6 (1966), 1219–1222 | MR | Zbl

[3] Zakharov V. E., Shabat A. B., “Tochnaya teoriya dvumernoi samofokusirovki i odnomernoi avtomodulyatsii voln v nelineinykh sredakh”, Zhurn. eksperiment. i teor. fiziki, 61:1 (1971), 118–134 | MR

[4] Nizhnik L. P., Fam Loi Vu, “Obratnaya zadacha rasseyaniya na poluosi s nesamosopryazhennoi potentsialnoi matritsei”, Ukr. mat. zhurn., 26:4 (1974), 469–486 | MR | Zbl

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

[6] Frolov I. S., “Obratnaya zadacha rasseyaniya dlya sistemy Diraka na vsei osi”, Dokl. AN SSSR, 207:1 (1972), 44–47 | Zbl

[7] Khasanov A. B., “Obratnaya zadacha teorii rasseyaniya dlya sistemy dvukh nesamosopryazhennykh differentsialnykh uravnenii pervogo poryadka”, Dokl. AN SSSR, 277:3 (1984), 559–562 | MR | Zbl

[8] Khasanov A. B., Urazboev G. U., “Metod resheniya uravneniya mKdF s samosoglasovannym istochnikom”, Uzbekskii mat. zhurn., 2003, no. 1, 69–75 | MR

[9] Khasanov A. B., Urazboev G. U., “Integrirovanie obschego uravneniya KdF s pravoi chastyu v klasse bystro ubyvayuschikh funktsii”, Uzbekskii mat. zhurn., 2003, no. 2, 53–59 | MR

[10] Ablowitz M. J., Kaup D. J., Newell A. C., Segur H., “The inverse scattering transform-Fourier analysis for nonlinear problems”, Stud. Appl. Math., 53:4 (1974), 249–315 | MR | Zbl

[11] Karpman V. I., “Solution evolution in the presence of perturbation”, Phys. Scripta, 20 (1979), 462–478 | DOI | MR | Zbl

[12] Mel'nikov V. K., “Integration of the nonlinear Schrödinger equation with source”, Inverse Problems, 8 (1992), 133–147 | DOI | MR

[13] Mel'nikov V. K., “Integrable and nonintegrable cases of the Lax equations with a source”, Theoret. and Math. Phys., 99:3 (1994), 733–737 | DOI | MR