Bifurcation analysis, and exact solutions of the two-mode Cahn–Allen equation by a novel variable coefficient auxiliary equation method
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255719" target="_blank" >RIV/61989100:27740/24:10255719 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S2211379724005679?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2211379724005679?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.rinp.2024.107882" target="_blank" >10.1016/j.rinp.2024.107882</a>
Alternative languages
Result language
angličtina
Original language name
Bifurcation analysis, and exact solutions of the two-mode Cahn–Allen equation by a novel variable coefficient auxiliary equation method
Original language description
This document elaborates on a newly introduced analytical method known as the "Variable Coefficient Generalized Abel Equation Method," as proposed by Hashemi in Hashemi (2024), designed specifically for addressing the two-mode Cahn-Allen equation. Diverging from conventional techniques that heavily rely on constant coefficient ordinary differential equations and auxiliary ordinary differential equations, our method innovatively incorporates variable coefficient ordinary differential equations within a sub-equation framework. Demonstrating its versatility, we apply this innovative technique to the two-mode Cahn-Allen equation, showcasing its effectiveness and efficiency through the derivation of analytical solutions. Notably, this method emerges as a promising tool for tackling complex nonlinear partial differential equations prevalent in fluid dynamics and wave propagation scenarios. Beyond merely expanding the repertoire of available analytical tools, our approach contributes to advancing solutions for various models within the realm of mathematical physics. Various forms of exact solutions, including exponential-type solutions, Kink solitons, dark solitons, and bright soliton solutions, are obtained for the model under consideration. Moreover, we delve into the analysis of bifurcation, chaotic behavior, and sensitivity within the context of the two-mode Cahn-Allen model, further enhancing the depth and breadth of our study. Three equilibria are analyzed across various classifications, including center point, focus point, saddle point, and node point. Chaotic behavior of the corresponding dynamical system is considered by adding the function ω1sin(ω2ζ). Lastly, sensitivity analysis of the system is conducted by examining different parameters of the model and imposing noise to the initial conditions. (C) 2024 The Author(s)
Czech name
—
Czech description
—
Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
—
OECD FORD branch
10300 - Physical sciences
Result continuities
Project
—
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
Results in Physics
ISSN
2211-3797
e-ISSN
—
Volume of the periodical
64
Issue of the periodical within the volume
September
Country of publishing house
US - UNITED STATES
Number of pages
11
Pages from-to
—
UT code for WoS article
—
EID of the result in the Scopus database
2-s2.0-85199766266