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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 44

Integration of the Negative Order Korteweg-de Vries Equation with a Special Source

Author(s)
Gayrat U. Urazboev1, Muzaffar M. Khasanov1, Iroda I. Baltaeva1

1Urgench State Univeresity, Urgench, Uzbekistan

Abstract
In this paper, we consider the negative order Korteweg-de Vries equation with a self-consistent source corresponding to the eigenvalues of the corresponding spectral problem. It is shown that the considered equation can be integrated by the method of the inverse spectral problem. The evolution of the spectral data of the Sturm-Liouville operator with a periodic potential associated with the solution of the considered equation is determined. The results obtained make it possible to apply the inverse problem method for solving the negative order Korteweg-de Vries equation with a self-consistent source corresponding to the eigenvalues of the corresponding spectral problem.
About the Authors

Gayrat U. Urazboev, Dr. Sci. (Phys.–Math.), Urgench State University, Urgench, 220100, Uzbekistan, gayrat71@mail.ru

Muzaffar M. Khasanov, Cand. Sci. (Phys.Math.), Assoc., Urgench State University, Urgench, 220100, Uzbekistan, hmuzaffar@mail.ru

Iroda I. Baltaeva, Cand. Sci. (Phys.Math.), Assoc., Urgench State University, Urgench, 220100, Uzbekistan, iroda-b@mail.ru

For citation
Urazboev G. U., Khasanov M. M., Baltaeva I. I. Integration of the Negative Order Korteweg-de Vries Equation with a Special Source. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 44, pp. 31–43. (in Russian) https://doi.org/10.26516/1997-7670.2023.44.31
Keywords
negative order Korteweg-de Vries equation, self-consistent source, inverse spectral problem, system of Dubrovin-Trubovitz equations, trace formulas
UDC
517.946
MSC
35P25, 35P30, 35Q51, 35Q53, 37K15
DOI
https://doi.org/10.26516/1997-7670.2023.44.31
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