Dynamical transitions and multistability in nonlinear wave systems: dual analytical insights into the geophysical Korteweg-de Vries Equation
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Dynamical transitions and multistability in nonlinear wave systems: dual analytical insights into the geophysical Korteweg-de Vries Equation
Original language description
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'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 & eacute; maps, and the computation of Lyapunov exponents. Additionally, a comprehensive multistability analysis reveals the system'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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
21100 - Other engineering and technologies
Result continuities
Project
<a href="/en/project/EH23_021%2F0008759" target="_blank" >EH23_021/0008759: Increasing the resilience of power grids in the context of decarbonisation, decentralisation and sustainable socio-economic development</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Modeling Earth Systems and Environment
ISSN
2363-6203
e-ISSN
2363-6211
Volume of the periodical
11
Issue of the periodical within the volume
6
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
384
UT code for WoS article
001551275000001
EID of the result in the Scopus database
2-s2.0-105013263354