Symmetry and complexity: a Lie symmetry method to bifurcation, chaos, multistability and soliton solutions of the nonlinear generalized advection-diffusion-reaction equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255147" target="_blank" >RIV/61989100:27740/24:10255147 - isvavai.cz</a>
Result on the web
<a href="http://10.1088/1402-4896/ad4fed" target="_blank" >http://10.1088/1402-4896/ad4fed</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1402-4896/ad4fed" target="_blank" >10.1088/1402-4896/ad4fed</a>
Alternative languages
Result language
angličtina
Original language name
Symmetry and complexity: a Lie symmetry method to bifurcation, chaos, multistability and soliton solutions of the nonlinear generalized advection-diffusion-reaction equation
Original language description
This paper deals with the complexities of nonlinear dynamics within the nonlinear generalized advection-diffusion-reaction equation, which describes intricate transport phenomena involving advection, diffusion, and reaction processes occurring simultaneously. Through the utilization of the Lie symmetry approach, we thoroughly examine this proposed model, transforming the partial differential equation into an ordinary differential equation using similarity reduction techniques to facilitate a more comprehensive analysis. Exact solutions for this transformed equation are derived employing the extended simplest equation method and the new extended direct algebraic method. To enhance understanding, contour plots along with 2D and 3D visualizations of solutions are employed. Additionally, we explore bifurcation and chaotic behaviors through a qualitative analysis of the model. Phase portraits are meticulously scrutinized across various parameter values, offering insights into system behavior. The introduction of an external periodic strength allows us to utilize various tools including time series, 3D, and 2D phase patterns to discern chaotic and quasi-periodic behaviors. Furthermore, a multistability analysis is conducted to examine the impacts of diverse initial conditions. These findings underscore the efficacy and practicality of the proposed methodologies in evaluating soliton solutions and elucidating phase dynamics across a spectrum of nonlinear models, offering novel perspectives on intricate physical phenomena
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science 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
Physica Scripta
ISSN
0031-8949
e-ISSN
1402-4896
Volume of the periodical
99
Issue of the periodical within the volume
7
Country of publishing house
GB - UNITED KINGDOM
Number of pages
23
Pages from-to
—
UT code for WoS article
001249936800001
EID of the result in the Scopus database
2-s2.0-85195540764