Analyzing sensitivity and multi-soliton solutions in the Estevez-Mansfield-Clarkson equation: Insights into dynamics of bifurcation and chaos

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255205" target="_blank" >RIV/61989100:27740/24:10255205 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2666818124002122?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2666818124002122?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.padiff.2024.100826" target="_blank" >10.1016/j.padiff.2024.100826</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Analyzing sensitivity and multi-soliton solutions in the Estevez-Mansfield-Clarkson equation: Insights into dynamics of bifurcation and chaos

Popis výsledku v původním jazyce

In this investigation, an analysis of the Estevez-Mansfield-Clarkson equation, a model equation employed in the examination of shape formation in liquid drops, optics, and mathematical physics, is undertaken. Firstly, multiple wave solitons, including 1-soliton, 2-soliton, and 3-soliton structures, are successfully generated through the utilization of a multiple exp-function technique. Subsequently, the conversion of the partial differential equation into an ordinary differential equation is executed. The extraction of various traveling wave patterns, such as kink, anti-kink, periodic, and exponential functions, is then carried out using the new auxiliary equation method. The outcomes are visually represented through 3-dimensional, 2-dimensional, and density plots, employing Mathematica software. Following this, an investigation into the qualitative dynamics of the equation is conducted, examining aspects such as bifurcation and chaos. Critical points are identified for bifurcation, and the dynamical system undergoes an outward force, resulting in the identification of chaotic patterns. Furthermore, the model&apos;s sensitivity across different initial values is explored. These solutions hold immense significance in the domains of nonlinear fiber optics and telecommunications that help in deepening our knowledge about the basic physical model. (C) 2024 The Author(s)

Název v anglickém jazyce

Analyzing sensitivity and multi-soliton solutions in the Estevez-Mansfield-Clarkson equation: Insights into dynamics of bifurcation and chaos

Popis výsledku anglicky

In this investigation, an analysis of the Estevez-Mansfield-Clarkson equation, a model equation employed in the examination of shape formation in liquid drops, optics, and mathematical physics, is undertaken. Firstly, multiple wave solitons, including 1-soliton, 2-soliton, and 3-soliton structures, are successfully generated through the utilization of a multiple exp-function technique. Subsequently, the conversion of the partial differential equation into an ordinary differential equation is executed. The extraction of various traveling wave patterns, such as kink, anti-kink, periodic, and exponential functions, is then carried out using the new auxiliary equation method. The outcomes are visually represented through 3-dimensional, 2-dimensional, and density plots, employing Mathematica software. Following this, an investigation into the qualitative dynamics of the equation is conducted, examining aspects such as bifurcation and chaos. Critical points are identified for bifurcation, and the dynamical system undergoes an outward force, resulting in the identification of chaotic patterns. Furthermore, the model&apos;s sensitivity across different initial values is explored. These solutions hold immense significance in the domains of nonlinear fiber optics and telecommunications that help in deepening our knowledge about the basic physical model. (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

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

—

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85199515690