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Teoreticheskaya i Matematicheskaya Fizika, 2001, Volume 129, Number 1, Pages 38–54
DOI: https://doi.org/10.4213/tmf518
(Mi tmf518)
 

This article is cited in 32 scientific papers (total in 32 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
References:
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.
Received: 16.12.2000
English version:
Theoretical and Mathematical Physics, 2001, Volume 129, Issue 1, Pages 1341–1356
DOI: https://doi.org/10.1023/A:1012463310382
Bibliographic databases:
Language: Russian
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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Linking options:
  • https://www.mathnet.ru/eng/tmf518
  • https://doi.org/10.4213/tmf518
  • https://www.mathnet.ru/eng/tmf/v129/i1/p38
  • This publication is cited in the following 32 articles:
    1. Gayrat U. Urazboev, Iroda I. Baltaeva, Shoira E. Atanazarova, “Soliton solutions of the negative order modified Korteweg – de Vries equation”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 47 (2024), 63–77  mathnet  crossref
    2. Bazar Babajanov, Michal Fečkan, Aygul Babadjanova, “On the Differential-Difference Sine-Gordon Equation with an Integral Type Source”, Mathematica Slovaca, 73:6 (2023), 1499  crossref
    3. Yuqin Yao, Hui Zhou, Fei Li, “The integrability, equivalence and solutions of two kinds of integrable deformed fourth-order matrix NLS equations”, Nonlinear Dyn, 111:9 (2023), 8673  crossref
    4. F. Li, Yuqin Yao, “Multisoliton and rational solutions for the extended fifth-order KdV equation in fluids with self-consistent sources”, Theoret. and Math. Phys., 210:2 (2022), 184–197  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    5. B. A. Babajanov, A. K. Babadjanova, A. Sh. Azamatov, “Integration of the differential–difference sine-Gordon equation with a self-consistent source”, Theoret. and Math. Phys., 210:3 (2022), 327–336  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    6. G. U. Urazboev, M. M. Khasanov, “Integrirovanie uravneniya Kortevega-de Friza otritsatelnogo poryadka s samosoglasovannym istochnikom v klasse periodicheskikh funktsii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:2 (2022), 228–239  mathnet  crossref  mathscinet
    7. A. A. Reyimberganov, I. D. Rakhimov, “The soliton solutions for the nonlinear Schrödinger equation with self-consistent source”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 36 (2021), 84–94  mathnet  crossref
    8. Hasanov A.B. Hoitmetov U.A., “On Integration of the Loaded Korteweg-de Vries Equation in the Class of Rapidly Decreasing Functions”, Proc. Inst. Math. Mech., 47:2 (2021), 250–261  mathscinet  isi
    9. K. A. Mamedov, “Integration of mKdV equation with a self-consistent source in the class of finite density functions in the case of moving eigenvalues”, Russian Math. (Iz. VUZ), 64:10 (2020), 66–78  mathnet  crossref  crossref  isi
    10. 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
    11. 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
    12. 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
    13. 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
    14. 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
    15. 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
    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. “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
    19. 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
    20. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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