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This article is cited in 23 scientific papers (total in 23 papers)
Integrating the Korteweg–de Vries Equation with a Self-Consistent Source and “Steplike” Initial Data
G. U. Urazboev, A. B. Khasanov
Al-Kharezmi Urgench State University, Khorezm, Uzbekistan
Abstract:
It is shown that “steplike” solutions of the Korteweg–de Vries equation with a self-consistent source can be found by the inverse scattering method for the Sturm–Liouville operator on the entire real line.
DOI:
https://doi.org/10.4213/tmf518
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English version:
Theoretical and Mathematical Physics, 2001, 129:1, 1341–1356
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Received: 16.12.2000
Citation:
G. U. Urazboev, A. B. Khasanov, “Integrating the Korteweg–de Vries Equation with a Self-Consistent Source and “Steplike” Initial Data”, TMF, 129:1 (2001), 38–54; Theoret. and Math. Phys., 129:1 (2001), 1341–1356
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/tmf518https://doi.org/10.4213/tmf518 http://mi.mathnet.ru/eng/tmf/v129/i1/p38
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Zhang, DJ, “The N-soliton solutions of the sine-Gordon equation with self-consistent sources”, Physica A-Statistical Mechanics and Its Applications, 321:3–4 (2003), 467
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Deng S.F., Chen D.Y., Zhang D.J., “The multisoliton solutions of the KP equation with self-consistent sources”, Nonlinear Evolution Equations and Dynamical Systems, 2003, 25–32
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A. B. Khasanov, G. U. Urazboev, “The solution of general KdV equation in a class of steplike functions”, J. Math. Sci. (N. Y.), 136:1 (2006), 3625–3640
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Khasanov, AB, “On the general Korteweg-de Vries equation with a source in the class of steplike functions”, Doklady Mathematics, 70:1 (2004), 512
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Hu, XB, “Construction of dKP and BKP equations with self-consistent sources”, Inverse Problems, 22:5 (2006), 1903
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Sun, YP, “On the non-isospectral Kadomtsev-Petviashvili equation with self-consistent sources”, Nonlinear Analysis-Theory Methods & Applications, 70:4 (2009), 1610
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A. B. Khasanov, A. B. Yakhshimuratov, “The Korteweg–de Vries equation with a self-consistent source in the class of periodic functions”, Theoret. and Math. Phys., 164:2 (2010), 1008–1015
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A. B. Yakhshimuratov, “Integrirovanie uravneniya Kortevega-de Friza so spetsialnym svobodnym chlenom v klasse periodicheskikh funktsii”, Ufimsk. matem. zhurn., 3:4 (2011), 144–150
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Urazboev G., “Integrating the Toda Lattice with Self-Consistent Source via Inverse Scattering Method”, Math. Phys. Anal. Geom., 15:4 (2012), 401–412
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M. M. Matyoqubov, A. B. Yakhshimuratov, “Integration of higher Korteweg-de Vries equation with a self-consistent source in class of periodic functions”, Ufa Math. J., 5:1 (2013), 102–111
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A. B. Yakhshimuratov, M. M. Matyokubov, “Integration of loaded Korteweg–de Vries equation in a class of periodic functions”, Russian Math. (Iz. VUZ), 60:2 (2016), 72–76
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