Investigating optical soliton pattern and dynamical analysis of Lonngren wave equation via phase portraits

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255710" target="_blank" >RIV/61989100:27740/24:10255710 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2666818124002481" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2666818124002481</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.padiff.2024.100862" target="_blank" >10.1016/j.padiff.2024.100862</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Investigating optical soliton pattern and dynamical analysis of Lonngren wave equation via phase portraits

Popis výsledku v původním jazyce

This study focuses on finding effective solutions to a mathematical equation known as the Lonngren wave equation. The solutions from the Lonngren wave equation can be used to evaluate electromagnetic signals in cable lines and sound waves in stochastic systems. The main equation is transformed into an ordinary differential equation by utilizing a suitable wave transformation, allowing for the exploration of mathematical models by using the modified Khater technique to detect the exact solution of a solitary wave. We use the provided method to derive the trigonometric, rational, and hyperbolic solutions. To illustrate the model&apos;s physical behavior, we also present graphical plots of selected solutions to illustrate the physical behavior of the model. By choosing appropriate values for arbitrary factors, the visual representation enhances the understanding of the dynamical system. Furthermore, the system is transformed into a planar dynamical system, and phase portrait analysis is conducted. Additionally, the sensitivity analysis of the dynamical system confirms that slight changes in the initial conditions will have minimal impact on the stability of the solution. The existence of chaotic dynamics in the Lonngren wave equation is explored by introducing a perturbed term in the dynamical system. Two and three-dimensional phase portraits will be used to demonstrate these chaotic behaviors. (C) 2024 The Author(s)

Název v anglickém jazyce

Investigating optical soliton pattern and dynamical analysis of Lonngren wave equation via phase portraits

Popis výsledku anglicky

This study focuses on finding effective solutions to a mathematical equation known as the Lonngren wave equation. The solutions from the Lonngren wave equation can be used to evaluate electromagnetic signals in cable lines and sound waves in stochastic systems. The main equation is transformed into an ordinary differential equation by utilizing a suitable wave transformation, allowing for the exploration of mathematical models by using the modified Khater technique to detect the exact solution of a solitary wave. We use the provided method to derive the trigonometric, rational, and hyperbolic solutions. To illustrate the model&apos;s physical behavior, we also present graphical plots of selected solutions to illustrate the physical behavior of the model. By choosing appropriate values for arbitrary factors, the visual representation enhances the understanding of the dynamical system. Furthermore, the system is transformed into a planar dynamical system, and phase portrait analysis is conducted. Additionally, the sensitivity analysis of the dynamical system confirms that slight changes in the initial conditions will have minimal impact on the stability of the solution. The existence of chaotic dynamics in the Lonngren wave equation is explored by introducing a perturbed term in the dynamical system. Two and three-dimensional phase portraits will be used to demonstrate these chaotic behaviors. (C) 2024 The Author(s)

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

11

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

12

Strana od-do

—

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85200910842