Geodesic
The Korteweg–de Vries equation with a self-consistent source in the class of periodic functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 214-221

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We use the inverse spectral problem method to integrate the Korteweg–de Vries equation with a self-consistent source in the class of periodic functions.
Keywords: Sturm–Liouville operator, spectral data, system of Dubrovin equations, Korteweg–de Vries equation with a self-consistent source. 
A. B. Khasanov; A. B. Yakhshimuratov. The Korteweg–de Vries equation with a self-consistent source in the class of periodic functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 214-221. http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a3/
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[1] S. P. Novikov, Funkts. analiz i ego pril., 8:3 (1974), 54–66 | DOI | MR | Zbl

[2] B. A. Dubrovin, Funkts. analiz i ego pril., 9:3 (1975), 41–51 | DOI | MR | Zbl

[3] B. A. Dubrovin, S. P. Novikov, ZhETF, 67:12 (1974), 2131–2143 | MR

[4] A. R. Its, V. B. Matveev, TMF, 23:1 (1975), 51–68 | DOI | MR

[5] P. D. Lax, “Periodic solutions of the KdV equations”, Nonlinear Wave Motion, Lecture Appl. Math., 15, eds. A. C. Newell, AMS, Providence, RI, 1974, 85–96 | MR | Zbl

[6] P. D. Lax, Comm. Pure Appl. Math., 28 (1975), 141–188 | DOI | MR | Zbl

[7] H. P. McKean, E. Trubowitz, Comm. Pure Appl. Math., 29:2 (1976), 143–226 | DOI | MR | Zbl

[8] V. A. Marchenko, Matem. sb., 95(137):3(11) (1974), 331–356 | DOI | MR | Zbl

[9] V. K. Melnikov, Metod integrirovaniya uravneniya Kortevega–de Vrisa s samosoglasovannym istochnikom, Preprint, OIYaI, Dubna, 1988 | MR

[10] V. K. Mel'nikov, Inverse Problems, 8:1 (1992), 133–147 | DOI | MR | Zbl

[11] J. Leon, A. Latifi, J. Phys. A, 23:8 (1990), 1385–1403 | DOI | MR | Zbl

[12] G. U. Urazboev, A. B. Khasanov, TMF, 129:1 (2001), 38–54 | DOI | MR | Zbl

[13] A. B. Khasanov, G. U. Urazboev, Uzb. matem. zhurn., 2003, no. 2, 53–59 | MR

[14] P. G. Grinevich, I. A. Taimanov, “Spectral conservation laws for periodic nonlinear equations of the Melnikov type”, Geometry, Topology, and Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, 224, eds. V. M. Buchstaber, I. M. Krichever, AMS, Providence, RI, 2008, 125–138 | MR | Zbl

[15] A. Yu. Orlov, E. I. Schulman, Lett. Math. Phys., 12:3 (1986), 171–179 | DOI | MR | Zbl