Classical and nonclassical Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to a 3D-modified nonlinear wave equation in liquid involving gas bubbles

The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving...

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Vydáno v:Boundary value problems Ročník 2024; číslo 1; s. 111 - 25
Hlavní autoři: Alizadeh, Farzaneh, Hosseini, Kamyar, Sirisubtawee, Sekson, Hincal, Evren
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 12.09.2024
Hindawi Limited
SpringerOpen
Témata:
3D-modified nonlinear wave equation
Analysis
Approximations and Expansions
Bifurcation analysis
Bifurcation theory
Classical and nonclassical Lie symmetries
Difference and Functional Equations
Dynamic systems theory
Dynamical systems
Elliptic functions
Exact solutions
Fluid dynamics
Impact analysis
Invariant solutions
Jacobi elliptic function solutions
Mathematics
Mathematics and Statistics
Nonlinear dynamics
Ordinary Differential Equations
Parameter modification
Partial Differential Equations
Physical properties
Plasma physics
Solitary waves
System theory
Wave equations
Jacobi elliptic function solutions
Invariant solutions
3D-modified nonlinear wave equation
Bifurcation analysis
76M60
Classical and nonclassical Lie symmetries
35C08
35A09
35C07
ISSN:1687-2770, 1687-2762, 1687-2770
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Shrnutí:The current paper undertakes an in-depth exploration of the dynamics of nonlinear waves governed by a 3D-modified nonlinear wave equation, a significant model in the study of complex wave phenomena. To this end, the study employs both classical and nonclassical Lie symmetries for rigorously deriving invariant solutions of the governing equation. These symmetries enable the formal construction of exact solutions, which are crucial for understanding the complex behavior of the model. Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory. Such an analysis reveals the conditions under which the 3D-modified nonlinear wave equation admits Jacobi elliptic function solutions. The study also delves into the impact of the nonlinear parameter on the physical characteristics of bright and kink solitary waves as well as continuous periodic waves using Maple. Overall, the comprehensive analysis presented not only enhances the understanding of complex nonlinear wave dynamics but also sets the stage for future advancements in vast areas of fluid dynamics and plasma physics.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-024-01921-8