Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods
Guardado en:
| Publicado en: | Symmetry vol. 17, no. 8 (2025), p. 1218-1240 |
|---|---|
| Autor principal: | |
| Otros Autores: | , , , |
| Publicado: |
MDPI AG
|
| Materias: | |
| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
| Etiquetas: |
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
MARC
| LEADER | 00000nab a2200000uu 4500 | ||
|---|---|---|---|
| 001 | 3244064203 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2073-8994 | ||
| 024 | 7 | |a 10.3390/sym17081218 |2 doi | |
| 035 | |a 3244064203 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 231635 |2 nlm | ||
| 100 | 1 | |a Majeed Zain |u Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan; zain.majeed@live.com (Z.M.); fazal.mahomed@wits.ac.za (F.M.M.) | |
| 245 | 1 | |a Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a In the present paper, a mathematical analysis of the Gardner equation with varying coefficients has been performed to give a more realistic model of physical phenomena, especially in regards to plasma physics. First, a Lie symmetry analysis was carried out, as a result of which a symmetry classification following the different representations of the variable coefficients was systematically derived. The reduced ordinary differential equation obtained is solved using the power-series method and solutions to the equation are represented graphically to give an idea of their dynamical behavior. Moreover, a fully connected neural network has been included as an efficient computation method to deal with the complexity of the reduced equation, by using traveling-wave transformation. The validity and correctness of the solutions provided by the neural networks have been rigorously tested and the solutions provided by the neural networks have been thoroughly compared with those generated by the Runge–Kutta method, which is a conventional and well-recognized numerical method. The impact of a variation in the loss function of different coefficients has also been discussed, and it has also been found that the dispersive coefficient affects the convergence rate of the loss contribution considerably compared to the other coefficients. The results of the current work can be used to improve knowledge on the nonlinear dynamics of waves in plasma physics. They also show how efficient it is to combine the approaches, which consists in the use of analytical and semi-analytical methods and methods based on neural networks, to solve nonlinear differential equations with variable coefficients of a complex nature. | |
| 653 | |a Plasma | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Fluid dynamics | ||
| 653 | |a Water waves | ||
| 653 | |a Symmetry | ||
| 653 | |a Runge-Kutta method | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Plasma physics | ||
| 653 | |a Numerical methods | ||
| 653 | |a Optics | ||
| 653 | |a Propagation | ||
| 653 | |a Physics | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Neural networks | ||
| 653 | |a Charged particles | ||
| 653 | |a Nonlinear differential equations | ||
| 653 | |a Traveling waves | ||
| 653 | |a Classification | ||
| 653 | |a Energy dissipation | ||
| 653 | |a Methods | ||
| 653 | |a Complexity | ||
| 653 | |a Dynamical systems | ||
| 653 | |a Acoustics | ||
| 653 | |a Graphical representations | ||
| 653 | |a Fluid mechanics | ||
| 653 | |a Nonlinear dynamics | ||
| 653 | |a Ordinary differential equations | ||
| 700 | 1 | |a Jhangeer Adil |u IT4Innovations, VSB—Technical University of Ostrava, Poruba, 708 00 Ostrava, Czech Republic; adil.jhangeer@vsb.cz | |
| 700 | 1 | |a Mahomed, F M |u Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan; zain.majeed@live.com (Z.M.); fazal.mahomed@wits.ac.za (F.M.M.) | |
| 700 | 1 | |a Almusawa Hassan |u Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia | |
| 700 | 1 | |a Zaman, F D |u School of Mathematics, University of the Witwatersrand, Johannesburg 2050, South Africa; fiaz.zaman@wits.ac.za | |
| 773 | 0 | |t Symmetry |g vol. 17, no. 8 (2025), p. 1218-1240 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3244064203/abstract/embedded/CH9WPLCLQHQD1J4S?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3244064203/fulltextwithgraphics/embedded/CH9WPLCLQHQD1J4S?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3244064203/fulltextPDF/embedded/CH9WPLCLQHQD1J4S?source=fedsrch |