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TMF, 2001, Volume 129, Number 1, Pages 38–54 (Mi tmf518)  

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

Bibliographic databases:

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zhang, DJ, “The N-soliton solutions for the modified KdV equation with self-consistent sources”, Journal of the Physical Society of Japan, 71:11 (2002), 2649  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Deng, SF, “The multisoliton solutions of the KP equation with self-consistent sources”, Journal of the Physical Society of Japan, 72:9 (2003), 2184  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Zhang, DJ, “The N-soliton solutions of some soliton equations with self-consistent sources”, Chaos Solitons & Fractals, 18:1 (2003), 31  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. 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  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. 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  crossref  mathscinet  zmath  isi
    6. 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  mathnet  crossref  mathscinet  zmath  elib
    7. Khasanov, AB, “On the general Korteweg-de Vries equation with a source in the class of steplike functions”, Doklady Mathematics, 70:1 (2004), 512  mathscinet  zmath  isi
    8. Hao, HH, “Double Wronskian soliton solution for mixed AKNS system”, Chinese Physics Letters, 22:12 (2005), 2987  crossref  adsnasa  isi  scopus  scopus
    9. Hu, XB, “Construction of dKP and BKP equations with self-consistent sources”, Inverse Problems, 22:5 (2006), 1903  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Runliang Lin, Haishen Yao, Yunbo Zeng, “Restricted Flows and the Soliton Equation with Self-Consistent Sources”, SIGMA, 2 (2006), 096, 8 pp.  mathnet  crossref  mathscinet  zmath
    11. “On the two-dimensional Leznov lattice equation with self-consistent sources”, Journal of Physics A-Mathematical and Theoretical, 40:42 (2007), 12691  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. Wang, HY, “Pfaffian solution of a semi-discrete BKP-type equation and its source generation version”, Journal of Physics A-Mathematical and Theoretical, 40:44 (2007), 13385  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Wang, HY, “Integrability of the semi-discrete Toda equation with self-consistent sources”, Journal of Mathematical Analysis and Applications, 330:2 (2007), 1128  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Wang, HY, “2D Toda lattice equation with self-consistent sources: Casoratian type solutions, bilinear Backlund transformation and Lax pair”, Journal of Computational and Applied Mathematics, 202:1 (2007), 133  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    15. Wang, HY, “A (2+1)-dimensional Sasa-Satsuma equation with self-consistent sources”, Journal of the Physical Society of Japan, 76:2 (2007), 024007  crossref  adsnasa  isi  scopus  scopus
    16. G. U. Urazboev, “Toda lattice with a special self-consistent source”, Theoret. and Math. Phys., 154:2 (2008), 260–269  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    17. Wang, HY, “On the Pfaffianized-KP equation with self-consistent sources”, Journal of Mathematical Analysis and Applications, 338:1 (2008), 82  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    18. Sun, YP, “On the non-isospectral Kadomtsev-Petviashvili equation with self-consistent sources”, Nonlinear Analysis-Theory Methods & Applications, 70:4 (2009), 1610  crossref  mathscinet  zmath  isi  scopus  scopus
    19. 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  mathnet  crossref  crossref  adsnasa  isi
    20. A. B. Yakhshimuratov, “Integrirovanie uravneniya Kortevega-de Friza so spetsialnym svobodnym chlenom v klasse periodicheskikh funktsii”, Ufimsk. matem. zhurn., 3:4 (2011), 144–150  mathnet  zmath
    21. Urazboev G., “Integrating the Toda Lattice with Self-Consistent Source via Inverse Scattering Method”, Math. Phys. Anal. Geom., 15:4 (2012), 401–412  crossref  mathscinet  zmath  isi  scopus  scopus
    22. 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  mathnet  crossref  mathscinet  elib
    23. 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  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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