An analytical investigation of the Van Der Waals gas system: Dynamics insights into bifurcation, optical pattern along with sensitivity and chaotic analysis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10256386" target="_blank" >RIV/61989100:27740/24:10256386 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2666818124003693?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2666818124003693?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.padiff.2024.100983" target="_blank" >10.1016/j.padiff.2024.100983</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An analytical investigation of the Van Der Waals gas system: Dynamics insights into bifurcation, optical pattern along with sensitivity and chaotic analysis

Popis výsledku v původním jazyce

This paper focuses on obtaining exact solutions for the nonlinear Van der Waals gas system using the modified Khater method. Renowned as one of the latest and most precise analytical schemes for nonlinear evolution equations, this method has proven its efficacy by generating diverse solutions for the model under consideration. The governing equation is transformed into an ordinary differential equation through a well-suited wave transformation. This analytical simplification makes it possible to use the provided methods to derive trigonometric, rational, and hyperbolic solutions. To illuminate the physical behavior of the model, graphical plots of selected solutions are presented. By selecting appropriate values for arbitrary factors, this visual representation enhances comprehension of the dynamical system. Furthermore, the system undergoes a certain transformation to become a planar dynamical system, and the bifurcation analysis is examined. Additionally, the sensitivity analysis of the dynamical system is conducted using the Runge–Kutta method to confirm that slight alterations in the initial conditions have minimal impact on the stability of the solution. The presence of chaotic dynamics in the Van der Waals gas system is explored by introducing a perturbed term in the dynamical system. Two and three-dimensional phase profiles are used to illustrate these chaotic behaviors. © 2024

Název v anglickém jazyce

An analytical investigation of the Van Der Waals gas system: Dynamics insights into bifurcation, optical pattern along with sensitivity and chaotic analysis

Popis výsledku anglicky

This paper focuses on obtaining exact solutions for the nonlinear Van der Waals gas system using the modified Khater method. Renowned as one of the latest and most precise analytical schemes for nonlinear evolution equations, this method has proven its efficacy by generating diverse solutions for the model under consideration. The governing equation is transformed into an ordinary differential equation through a well-suited wave transformation. This analytical simplification makes it possible to use the provided methods to derive trigonometric, rational, and hyperbolic solutions. To illuminate the physical behavior of the model, graphical plots of selected solutions are presented. By selecting appropriate values for arbitrary factors, this visual representation enhances comprehension of the dynamical system. Furthermore, the system undergoes a certain transformation to become a planar dynamical system, and the bifurcation analysis is examined. Additionally, the sensitivity analysis of the dynamical system is conducted using the Runge–Kutta method to confirm that slight alterations in the initial conditions have minimal impact on the stability of the solution. The presence of chaotic dynamics in the Van der Waals gas system is explored by introducing a perturbed term in the dynamical system. Two and three-dimensional phase profiles are used to illustrate these chaotic behaviors. © 2024

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Partial Differential Equations in Applied Mathematics

ISSN

2666-8181

e-ISSN

2666-8181

Svazek periodika

12

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

—

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85208562549