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Keywords = self-similar solitary wave

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14 pages, 1184 KiB  
Article
Solitary Waves and Their Interactions in the Cylindrical Korteweg–De Vries Equation
by Wencheng Hu, Jingli Ren and Yury Stepanyants
Symmetry 2023, 15(2), 413; https://doi.org/10.3390/sym15020413 - 3 Feb 2023
Cited by 10 | Viewed by 1883
Abstract
We consider approximate, exact, and numerical solutions to the cylindrical Korteweg–de Vries equation. We show that there are different types of solitary waves and obtain the dependence of their parameters on distance. Then, we study the interaction of solitary waves of different types. [...] Read more.
We consider approximate, exact, and numerical solutions to the cylindrical Korteweg–de Vries equation. We show that there are different types of solitary waves and obtain the dependence of their parameters on distance. Then, we study the interaction of solitary waves of different types. Full article
(This article belongs to the Special Issue Wave Processes in Fluids with Symmetric Density Stratification)
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15 pages, 1554 KiB  
Article
Solitary-like Wave Dynamics in Thin Liquid Films over a Vibrated Inclined Plane
by Ivan S. Maksymov and Andrey Pototsky
Appl. Sci. 2023, 13(3), 1888; https://doi.org/10.3390/app13031888 - 1 Feb 2023
Cited by 4 | Viewed by 1855
Abstract
Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in other physical systems. Here we investigate, experimentally and theoretically, the [...] Read more.
Solitary-like surface waves that originate from the spatio-temporal evolution of falling liquid films have been the subject of theoretical and experimental research due to their unique properties that are not readily observed in other physical systems. Here we investigate, experimentally and theoretically, the dynamics of solitary-like surface waves in a liquid layer on an inclined plane that is subjected to a harmonic low-frequency vibration in a range from 30 to 50 Hz. We employ a standard boundary layer model, which describes large-amplitude deformations of the film surface, assuming that it has a self-similar parabolic longitudinal flow velocity profile, to confirm the experimental results and to explain the interplay between the short-wavelength Faraday instability and long-wavelength gravitational instability. In particular, we demonstrate that the vibration results in a decrease in the average and peak amplitude of the long solitary-like surface waves. However, the speed of these waves remains largely unaffected by the vibration, implying that they may propagate over large distances almost without changing their amplitude, thus rendering them suitable for a number of practical applications, where the immunity of pulses that carry information to external vibrations is required. Full article
(This article belongs to the Section Fluid Science and Technology)
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