Harry Dym equation with a special self-consistent source
https://doi.org/10.22405/2226-8383-2025-26-5-246-258
Abstract
The work is concerned with studying the integration of the Harry Dym equation with the
self-consistent source. The source consists of the combination of the eigenfunctions and linear independent solution with the same eigenfunctions of the corresponding spectral problem for the string equation which has not spectral singularities. While considering the source, the points of the discrete spectrum of the string equation have been as the functions of time. Deduced the time performance of the scattering data of the string equation which allows to integrate the Cauchy problem for the Harry Dym equation with the special self-consistent source in the class of the rapidly decreasing functions via the inverse scattering method.
About the Authors
Gayrat Urazalievich Urazboev
Urgench State University named after Abu Rayhan Biruni; V. I. Romanovskiy Institute of Mathematics; Uzbekistan Academy of Sciences
Uzbekistan
Uzbekistan
doctor of physical and mathematical sciences
Aygul Kamildjanovna Babadjanova
V. I. Romanovskiy Institute of Mathematics; Uzbekistan Academy of Sciences; Urgench State
University named after Abu Rayhan Biruni
Uzbekistan
Uzbekistan
candidate of physical and mathematical sciences
Shoira Erkinovna Atanazarova
V. I. Romanovskiy Institute of Mathematics; Uzbekistan Academy of Sciences; Urgench State University named after Abu Rayhan Biruni
Uzbekistan
Uzbekistan
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Review
For citations:
Urazboev G.U., Babadjanova A.K., Atanazarova Sh.E. Harry Dym equation with a special self-consistent source. Chebyshevskii Sbornik. 2025;26(5):246-258. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-5-246-258
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