A Modified Analytical Data-Mapping Framework for Symmetric Multiscale Soliton and Chaotic Dynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10259593" target="_blank" >RIV/61989100:27740/25:10259593 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2073-8994/17/11/1963" target="_blank" >https://www.mdpi.com/2073-8994/17/11/1963</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym17111963" target="_blank" >10.3390/sym17111963</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Modified Analytical Data-Mapping Framework for Symmetric Multiscale Soliton and Chaotic Dynamics

Popis výsledku v původním jazyce

The (3 + 1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff equation, a model that describes long-wave interactions and has numerous applications in mathematics, engineering, and physics, is examined in this work. First, a wave transformation is used to reduce the equation to lower dimensions. The modified Khater method is then used to derive different types of solitary wave solutions, such as chirped, kink, periodic, and kink-bright types. By allocating suitable constant parameters, 3D, 2D, and contour plots are created to demonstrate the physical behavior of these solutions. Phase portraits are used to qualitatively analyze the undisturbed planar system using bifurcation theory. The system is then perturbed by an external force, resulting in chaotic dynamics. Chaos in the system is confirmed using multiple diagnostic tools, including time series plots, Poincar &amp; eacute; sections, chaotic attractors, return maps, bifurcation diagrams, power spectra, and Lyapunov exponents. The stability of the model is further investigated with varying initial conditions. A bidirectional scatter plot technique, which efficiently reveals overlapping regions using data point distributions, is presented for comparing solution behaviors. Overall, this work offers useful tools for advancing applied mathematics research as well as a deeper understanding of nonlinear wave dynamics.

Název v anglickém jazyce

A Modified Analytical Data-Mapping Framework for Symmetric Multiscale Soliton and Chaotic Dynamics

Popis výsledku anglicky

The (3 + 1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff equation, a model that describes long-wave interactions and has numerous applications in mathematics, engineering, and physics, is examined in this work. First, a wave transformation is used to reduce the equation to lower dimensions. The modified Khater method is then used to derive different types of solitary wave solutions, such as chirped, kink, periodic, and kink-bright types. By allocating suitable constant parameters, 3D, 2D, and contour plots are created to demonstrate the physical behavior of these solutions. Phase portraits are used to qualitatively analyze the undisturbed planar system using bifurcation theory. The system is then perturbed by an external force, resulting in chaotic dynamics. Chaos in the system is confirmed using multiple diagnostic tools, including time series plots, Poincar &amp; eacute; sections, chaotic attractors, return maps, bifurcation diagrams, power spectra, and Lyapunov exponents. The stability of the model is further investigated with varying initial conditions. A bidirectional scatter plot technique, which efficiently reveals overlapping regions using data point distributions, is presented for comparing solution behaviors. Overall, this work offers useful tools for advancing applied mathematics research as well as a deeper understanding of nonlinear wave dynamics.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

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

11

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

24

Strana od-do

1963

Kód UT WoS článku

001624478900001

EID výsledku v databázi Scopus

2-s2.0-105023370621