Multi-dimensional phase portraits of stochastic fractional derivatives for nonlinear dynamical systems with solitary wave formation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10254852" target="_blank" >RIV/61989100:27740/24:10254852 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11082-024-06347-1" target="_blank" >https://link.springer.com/article/10.1007/s11082-024-06347-1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11082-024-06347-1" target="_blank" >10.1007/s11082-024-06347-1</a>
Alternative languages
Result language
angličtina
Original language name
Multi-dimensional phase portraits of stochastic fractional derivatives for nonlinear dynamical systems with solitary wave formation
Original language description
This manuscript delves into the examination of the stochastic fractional derivative of Drinfel'd-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. In our study, the proposed equation is through examined through various viewpoints, encompassing soliton dynamics, bifurcation analysis, chaotic behaviors, and sensitivity analysis. A few dark and bright shaped soliton solutions, including the unperturbed term, are also examined, and the various 2D and 3D solitonic structures are computed using the Tanh-method. It is found that a saddle point bifurcation causes the transition from periodic behavior to quasi-periodic behavior in a sensitive area. Further analysis reveals favorable conditions for the multidimensional bifurcation of dynamic behavioral solutions. Different types of wave solutions are identified in certain solutions by entering numerous values for the parameters, demonstrating the effectiveness and precision of Tanh-methods. A planar dynamical system is then created using the Galilean transformation, with the actual model serving as a starting point. It is observed that a few physical criteria in the discussed equation exhibit more multi-stable properties, as many multi-stability structures are employed by some individuals. Moreover, sensitivity behavior is employed to examine perturbed dynamical systems across diverse initial conditions. The techniques and findings presented in this paper can be extended to investigate a broader spectrum of nonlinear 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
10100 - Mathematics
Result continuities
Project
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Continuities
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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
Optical And Quantum Electronics
ISSN
0306-8919
e-ISSN
1572-817X
Volume of the periodical
56
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
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UT code for WoS article
001195953300014
EID of the result in the Scopus database
2-s2.0-85188916390