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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 221, Number 2, Pages 298–314
DOI: https://doi.org/10.4213/tmf10769
(Mi tmf10769)
 

On the Hirota equation with a self-consistent source

A. B. Khasanova, A. A. Reyimberganovb

a Samarkand State University, Samarkand, Uzbekistan
b Urgench State University, Urgench, Uzbekistan
References:
Abstract: We develop the formalism of the inverse scattering problem method for the Cauchy problem for the defocusing Hirota equation with a self-consistent source. The specific feature of the considered Cauchy problem is that the solution is assumed to approach nonzero limits as the spatial variable approaches the plus and minus infinities. The purpose of the paper is to present two main steps of the formalism: first, the inverse problem for the associated linear Zakharov–Shabat system and, second, the evolution of the associated scattering data. A theorem is proved on the evolution of scattering data of a self-adjoint Zakharov–Shabat system, with the potential given by a solution of the defocusing Hirota equation with a self-consistent source.
Keywords: Hirota equation, inverse scattering transformation, self-consistent source, soliton solution, nonzero boundary condition.
Received: 06.06.2024
Revised: 16.07.2024
English version:
Theoretical and Mathematical Physics, 2024, Volume 221, Issue 2, Pages 1852–1866
DOI: https://doi.org/10.1134/S0040577924110059
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. B. Khasanov, A. A. Reyimberganov, “On the Hirota equation with a self-consistent source”, TMF, 221:2 (2024), 298–314; Theoret. and Math. Phys., 221:2 (2024), 1852–1866
Citation in format AMSBIB
\Bibitem{KhaRey24}
\by A.~B.~Khasanov, A.~A.~Reyimberganov
\paper On the~Hirota equation with a~self-consistent source
\jour TMF
\yr 2024
\vol 221
\issue 2
\pages 298--314
\mathnet{http://mi.mathnet.ru/tmf10769}
\crossref{https://doi.org/10.4213/tmf10769}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...221.1852K}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 221
\issue 2
\pages 1852--1866
\crossref{https://doi.org/10.1134/S0040577924110059}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85210233434}
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  • https://www.mathnet.ru/eng/tmf/v221/i2/p298
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