Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Comparative Analysis of the Gardner Equation in Plasma Physics Using Analytical and Neural Network Methods

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Symmetry

ISSN

2073-8994

e-ISSN

2073-8994

Svazek periodika

17

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

22

Strana od-do

1218

Kód UT WoS článku

001558315500001

EID výsledku v databázi Scopus

2-s2.0-105014390361