Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258428" target="_blank" >RIV/61989100:27740/25:10258428 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2073-8994/17/8/1218" target="_blank" >https://www.mdpi.com/2073-8994/17/8/1218</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym17081218" target="_blank" >10.3390/sym17081218</a>
Alternative languages
Result language
angličtina
Original language name
Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10300 - Physical sciences
Result continuities
Project
—
Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry
ISSN
2073-8994
e-ISSN
2073-8994
Volume of the periodical
17
Issue of the periodical within the volume
8
Country of publishing house
CH - SWITZERLAND
Number of pages
22
Pages from-to
1218
UT code for WoS article
001558315500001
EID of the result in the Scopus database
2-s2.0-105014390361