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

IF 1.7 4区 数学 Q1 Mathematics
Farzaneh Alizadeh, Kamyar Hosseini, Sekson Sirisubtawee, Evren Hincal
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引用次数: 0

Abstract

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.
涉及气泡的液体中三维修正非线性波方程的经典和非经典李对称性、分岔分析和雅可比椭圆函数解
本文深入探讨了由三维修正非线性波方程支配的非线性波的动力学,该方程是研究复杂波现象的一个重要模型。为此,研究采用了经典和非经典的李对称性来严格推导支配方程的不变解。这些对称性使得精确解的正式构建成为可能,而精确解对于理解模型的复杂行为至关重要。此外,研究还通过平面动力系统理论的应用扩展到了分岔分析领域。这种分析揭示了三维修正非线性波方程接受雅可比椭圆函数解的条件。研究还利用 Maple 深入探讨了非线性参数对亮波和扭结孤波以及连续周期波物理特性的影响。总之,所做的全面分析不仅增强了人们对复杂非线性波动力学的理解,还为未来在流体动力学和等离子体物理学的广泛领域取得进展奠定了基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
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