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...
Saved in:
| Main Authors: | , , , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849235433325592576 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-0d67decefe89479cb92a6d72cc05bb9c |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT ehabmalmetwally analysisofgasbubblingdynamicsvialiesymmetryapproachofnonlinearwaveequation AT rashasaleh analysisofgasbubblingdynamicsvialiesymmetryapproachofnonlinearwaveequation AT samahmmabrouk analysisofgasbubblingdynamicsvialiesymmetryapproachofnonlinearwaveequation AT ahmedsrashed analysisofgasbubblingdynamicsvialiesymmetryapproachofnonlinearwaveequation |