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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». 2024. Vol 50

Integration of the Loaded Negative Order Nonlinear Schrodinger Equation in the Class of Periodic Functions

Author(s)
Muzaffar M. Khasanov1, Ilkham D. Rakhimov1, Donyor B. Azimov1

1Urgench State University, Urgench, Uzbekistan

Abstract
In this paper, we consider the loaded negative order nonlinear Schrodinger equation (NSE) in the class of periodic functions. It is shown that the loaded negative order nonlinear Schrodinger equation can be integrated by the inverse spectral problem method. The evolution of the spectral data of the Dirac operator with a periodic potential associated with the solution of the loaded negative order nonlinear Schrodinger equation is determined. The results obtained make it possible to apply the inverse problem method to solve the loaded negative order nonlinear Schrodinger equation in the class of periodic ones. Important corollaries are obtained about the analyticity and period of the solution concerning the spatial variable.
About the Authors

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

Ilkham D. Rakhimov, Cand. Sci. (Phys.-Math.), Urgench State University, Urgench, 220100, Uzbekistan, ilxom@urdu.uz

Donyor B. Azimov, Master (Phys.-Math.), Junior Researcher, Urgench State University, Urgench, 220100, Uzbekistan, doniyor.azimov.97@bk.ru

For citation

Khasanov M. M., Rakhimov I. D., Azimov D. B. IIntegration of the Loaded Negative Order Nonlinear Schrodinger Equation in the Class of Periodic Functions. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 50, pp. 51–65.

https://doi.org/10.26516/1997-7670.2024.50.51

Keywords
loaded negative order nonlinear Schrodinger equation, soliton, Dirac operator, inverse spectral problem, Dubrovin’s system of equations, trace formulas
UDC
517.957
MSC
35P25, 35P30, 35Q51, 35Q53, 37K15
DOI
https://doi.org/10.26516/1997-7670.2024.50.51
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