A Comprehensive Study of Dynamical Behavior and Nonlinear Structures of the Modified α Equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10256168" target="_blank" >RIV/61989100:27740/24:10256168 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/12/23/3809" target="_blank" >https://www.mdpi.com/2227-7390/12/23/3809</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math12233809" target="_blank" >10.3390/math12233809</a>
Alternative languages
Result language
angličtina
Original language name
A Comprehensive Study of Dynamical Behavior and Nonlinear Structures of the Modified α Equation
Original language description
In this article, the modified alpha equation is solved using the direct algebraic approach. As a result, numerous new and more generalized exact solutions for such equations have been found, taking into account the wide range of travelling structures. The rational, trigonometric, hyperbolic, and exponential functions with a couple of licentious parameters are thus included in these exact answers. Analytical solutions feature a variety of physical structures, which are visually studied to demonstrate their dynamic behavior in 2D and 3D. Considering the parameters, all feasible phase portraits are shown. Furthermore, we used numerical approaches to determine the nonlinear periodic structures of the mentioned model, and the data are graphically displayed. Additionally, we employed numerical approaches to determine the nonlinear conditions that contribute to the presented model, and the data are graphically displayed. After evaluating the influence of frequency following the application of an external periodic factor, sensitivity exploration is used to study quasi-periodic and chaotic behavior for several starting value problems. Furthermore, the function of physical characteristics is investigated using an external periodic force. Quasi-periodic and quasi-periodic-chaotic patterns are described with the inclusion of a perturbation term. The direct algebraic methodology would be used to derive the soliton solution of modified alpha equation, from which the Galilean transformation derives traveling wave solutions of the considered and a bifurcation behavior is reported. Analytical and numerical methods have been used to have the condition of the travelling wave phase transformation. The well-judged values of parameters are enhanced well with a graphically formal analysis of such specific solutions to illustrate their propagation. Then a planer dynamical system is introduced, and a bifurcation analysis is utilized to identify the bifurcation structures of the dynamical model's nonlinear wave propagation solutions. Additionally, the periodic and quasi-periodic behavior of the discussed equation is analyzed using sensitivity analysis for a range of beginning values. To further comprehend the dynamical behaviors of the resultant solutions, a graphic analysis is conducted.
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
Mathematics
ISSN
2227-7390
e-ISSN
2227-7390
Volume of the periodical
12
Issue of the periodical within the volume
23
Country of publishing house
CH - SWITZERLAND
Number of pages
18
Pages from-to
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UT code for WoS article
001376353500001
EID of the result in the Scopus database
2-s2.0-85211813371