Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3+1)-Dimensional Wave Equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255137" target="_blank" >RIV/61989100:27740/24:10255137 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2073-8994/16/5/608" target="_blank" >https://www.mdpi.com/2073-8994/16/5/608</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym16050608" target="_blank" >10.3390/sym16050608</a>
Alternative languages
Result language
angličtina
Original language name
Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3+1)-Dimensional Wave Equation
Original language description
The examination of new (3 + 1)-dimensional wave equations is undertaken in this study. Initially, the identification of the Lie symmetries of the model is carried out through the utilization of the Lie symmetry approach. The commutator and adjoint table of the symmetries are presented. Subsequently, the model under discussion is transformed into an ordinary differential equation using these symmetries. The construction of several bright, kink, and dark solitons for the suggested equation is then achieved through the utilization of the new auxiliary equation method. Subsequently, an analysis of the dynamical nature of the model is conducted, encompassing various angles such as bifurcation, chaos, and sensitivity. Bifurcation occurs at critical points within a dynamical system, accompanied by the application of an outward force, which unveils the emergence of chaotic phenomena. Two-dimensional plots, time plots, multistability, and Lyapunov exponents are presented to illustrate these chaotic behaviors. Furthermore, the sensitivity of the investigated model is executed utilizing the Runge-Kutta method. This analysis confirms that the stability of the solution is minimally affected by small changes in initial conditions. The attained outcomes show the effectiveness of the presented methods in evaluating solitons of multiple nonlinear models.
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
10100 - Mathematics
Result continuities
Project
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Continuities
O - Projekt operacniho programu
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry
ISSN
2073-8994
e-ISSN
2073-8994
Volume of the periodical
16
Issue of the periodical within the volume
5
Country of publishing house
CH - SWITZERLAND
Number of pages
22
Pages from-to
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UT code for WoS article
001231486000001
EID of the result in the Scopus database
2-s2.0-85194085589