Dynamical transitions and multistability in nonlinear wave systems: dual analytical insights into the geophysical Korteweg-de Vries Equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258512" target="_blank" >RIV/61989100:27740/25:10258512 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s40808-025-02559-w#Sec1" target="_blank" >https://link.springer.com/article/10.1007/s40808-025-02559-w#Sec1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s40808-025-02559-w" target="_blank" >10.1007/s40808-025-02559-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dynamical transitions and multistability in nonlinear wave systems: dual analytical insights into the geophysical Korteweg-de Vries Equation

Popis výsledku v původním jazyce

This paper focuses on the (1+1)-dimensional geophysical Korteweg-de Vries equation to explain the complex behavior of nonlinear waves in different areas of mathematical physics, such as nonlinear optics, fluid dynamics, and plasma physics. Analytical solutions are obtained by employing two analytical techniques: the modified Khater method and the Sardar subequation technique. These techniques yield a variety of novel solutions for the system, which are systematically compared to enhance understanding of the underlying dynamics of the nonlinear model. The solutions include trigonometric, hyperbolic, rational, and Jacobi elliptic functions, providing a rich mathematical framework. Graphical simulations are presented to visualize the dynamical behavior of the obtained solutions, with 3D surface plots, 2D line graphs, and contour plots generated using software such as MATLAB and Mathematica. To further analyze the system&apos;s qualitative behavior, phase portrait analysis is carried out for the unperturbed planar form. When an external forcing term is introduced, the system exhibits complex dynamics and chaotic behavior. This chaotic nature is demonstrated using time series, two- and three-dimensional phase plots, Poincar &amp; eacute; maps, and the computation of Lyapunov exponents. Additionally, a comprehensive multistability analysis reveals the system&apos;s high sensitivity to initial conditions, where small perturbations can induce transitions between stable and unstable regimes. Numerical simulations using the Runge-Kutta method support the analytical findings and highlight the intricate dynamical behavior of the model. In general, the analytical and numerical techniques employed offer valuable tools for exploring and understanding a wide range of non-linear wave phenomena.

Název v anglickém jazyce

Dynamical transitions and multistability in nonlinear wave systems: dual analytical insights into the geophysical Korteweg-de Vries Equation

Popis výsledku anglicky

This paper focuses on the (1+1)-dimensional geophysical Korteweg-de Vries equation to explain the complex behavior of nonlinear waves in different areas of mathematical physics, such as nonlinear optics, fluid dynamics, and plasma physics. Analytical solutions are obtained by employing two analytical techniques: the modified Khater method and the Sardar subequation technique. These techniques yield a variety of novel solutions for the system, which are systematically compared to enhance understanding of the underlying dynamics of the nonlinear model. The solutions include trigonometric, hyperbolic, rational, and Jacobi elliptic functions, providing a rich mathematical framework. Graphical simulations are presented to visualize the dynamical behavior of the obtained solutions, with 3D surface plots, 2D line graphs, and contour plots generated using software such as MATLAB and Mathematica. To further analyze the system&apos;s qualitative behavior, phase portrait analysis is carried out for the unperturbed planar form. When an external forcing term is introduced, the system exhibits complex dynamics and chaotic behavior. This chaotic nature is demonstrated using time series, two- and three-dimensional phase plots, Poincar &amp; eacute; maps, and the computation of Lyapunov exponents. Additionally, a comprehensive multistability analysis reveals the system&apos;s high sensitivity to initial conditions, where small perturbations can induce transitions between stable and unstable regimes. Numerical simulations using the Runge-Kutta method support the analytical findings and highlight the intricate dynamical behavior of the model. In general, the analytical and numerical techniques employed offer valuable tools for exploring and understanding a wide range of non-linear wave phenomena.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

21100 - Other engineering and technologies

Projekt

<a href="/cs/project/EH23_021%2F0008759" target="_blank" >EH23_021/0008759: Zvýšení odolnosti energetických sítí v kontextu dekarbonizace, decentralizace a udržitelného socioekonomického rozvoje</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Modeling Earth Systems and Environment

ISSN

2363-6203

e-ISSN

2363-6211

Svazek periodika

11

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

23

Strana od-do

384

Kód UT WoS článku

001551275000001

EID výsledku v databázi Scopus

2-s2.0-105013263354