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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 214, Number 2, Pages 198–210
DOI: https://doi.org/10.4213/tmf10365 (Mi tmf10365) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Integrating the modified Korteweg–de Vries–sine-Gordon equation in the class of periodic infinite-gap functions

A. B. Khasanova, Kh. N. Normurodova, U. O. Hudayerovb

a Samarkand State University, Samarkand, Uzbekistan
b Samarkand Architectural and Construction Institute, Samarkand, Uzbekistan
Full-text PDF (450 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf10365
Abstract: The inverse spectral problem method is used to integrate the nonlinear modified Korteweg–de Vries–sine-Gordon equation in the class of periodic infinite-gap functions. The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of six-times continuously differentiable periodic infinite-gap functions is proved. It is shown that the sum of a uniformly converging functional series constructed with the use of a solution of a system of Dubrovin equations and the first trace formula satisfies the modified Korteweg–de Vries–sine-Gordon equation.
Keywords: modified Korteweg–de Vries–sine-Gordon equation, Dirac operator, spectral data, system of Dubrovin equations, trace formulas.
Received: 10.09.2022
Revised: 17.10.2022
English version:
Theoretical and Mathematical Physics, 2023, Volume 214, Issue 2, Pages 170–182
DOI: https://doi.org/10.1134/S0040577923020022
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. B. Khasanov, Kh. N. Normurodov, U. O. Hudayerov, “Integrating the modified Korteweg–de Vries–sine-Gordon equation in the class of periodic infinite-gap functions”, TMF, 214:2 (2023), 198–210; Theoret. and Math. Phys., 214:2 (2023), 170–182
Citation in format AMSBIB
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\by A.~B.~Khasanov, Kh.~N.~Normurodov, U.~O.~Hudayerov
\paper Integrating the~modified Korteweg--de~Vries--\allowbreak sine-Gordon equation in the~class of periodic infinite-gap functions
\jour TMF
\yr 2023
\vol 214
\issue 2
\pages 198--210
\mathnet{http://mi.mathnet.ru/tmf10365}
\crossref{https://doi.org/10.4213/tmf10365}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563401}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...214..170K}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 214
\issue 2
\pages 170--182
\crossref{https://doi.org/10.1134/S0040577923020022}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149314235}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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