Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation

Abstract Bubbles formed by the introduction of gas into a liquid are a common phenomenon, known as gas bubbling in liquids. This process is widely utilized in various industries for aeration, mixing, and purification. An optimal system of Lie symmetry analysis is employed to investigate the generali...

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Main Authors: Ehab M. Almetwally, Rasha Saleh, Samah M. Mabrouk, Ahmed S. Rashed
Format: Article
Language:English
Published: Nature Portfolio 2025-08-01
Series:Scientific Reports
Subjects:
Online Access:https://doi.org/10.1038/s41598-025-09588-6
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author Ehab M. Almetwally
Rasha Saleh
Samah M. Mabrouk
Ahmed S. Rashed
author_facet Ehab M. Almetwally
Rasha Saleh
Samah M. Mabrouk
Ahmed S. Rashed
author_sort Ehab M. Almetwally
collection DOAJ
description Abstract Bubbles formed by the introduction of gas into a liquid are a common phenomenon, known as gas bubbling in liquids. This process is widely utilized in various industries for aeration, mixing, and purification. An optimal system of Lie symmetry analysis is employed to investigate the generalized (3 + 1)-dimensional nonlinear wave equation (NLWE). Single, double, triple, and quadruple linear combinations are constructed to derive novel solutions that represent different dynamic and turbulent behaviors of the bubbles. This equation models a wide range of nonlinear phenomena occurring in liquids containing gas bubbles. The proposed methodology is used to obtain a diverse set of accurate soliton solutions to the equation. Furthermore, the resulting solutions are analyzed in terms of their physical interpretations.
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institution Kabale University
issn 2045-2322
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series Scientific Reports
spelling doaj-art-0d67decefe89479cb92a6d72cc05bb9c2025-08-20T04:02:46ZengNature PortfolioScientific Reports2045-23222025-08-0115112110.1038/s41598-025-09588-6Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equationEhab M. Almetwally0Rasha Saleh1Samah M. Mabrouk2Ahmed S. Rashed3Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU)Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig UniversityDepartment of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig UniversityDepartment of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig UniversityAbstract Bubbles formed by the introduction of gas into a liquid are a common phenomenon, known as gas bubbling in liquids. This process is widely utilized in various industries for aeration, mixing, and purification. An optimal system of Lie symmetry analysis is employed to investigate the generalized (3 + 1)-dimensional nonlinear wave equation (NLWE). Single, double, triple, and quadruple linear combinations are constructed to derive novel solutions that represent different dynamic and turbulent behaviors of the bubbles. This equation models a wide range of nonlinear phenomena occurring in liquids containing gas bubbles. The proposed methodology is used to obtain a diverse set of accurate soliton solutions to the equation. Furthermore, the resulting solutions are analyzed in terms of their physical interpretations.https://doi.org/10.1038/s41598-025-09588-6Nonlinear wave equationLie InfinitesimalsOptimal systemSolitons
spellingShingle Ehab M. Almetwally
Rasha Saleh
Samah M. Mabrouk
Ahmed S. Rashed
Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation
Scientific Reports
Nonlinear wave equation
Lie Infinitesimals
Optimal system
Solitons
title Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation
title_full Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation
title_fullStr Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation
title_full_unstemmed Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation
title_short Analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation
title_sort analysis of gas bubbling dynamics via lie symmetry approach of nonlinear wave equation
topic Nonlinear wave equation
Lie Infinitesimals
Optimal system
Solitons
url https://doi.org/10.1038/s41598-025-09588-6
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AT ahmedsrashed analysisofgasbubblingdynamicsvialiesymmetryapproachofnonlinearwaveequation