Exploring the Lie symmetries, conservation laws, bifurcation analysis and dynamical waveform patterns of diverse exact solution to the Klein–Gordan equation
IF 3.3 3区 工程技术Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
Tariq Mahmood, Ghadah Alhawael, Sonia Akram, Mati ur Rahman
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引用次数: 0
Abstract
This paper presents a comprehensive analysis of the \((1+1)\)-dimensional Klein-Gordan equation which plays a significant role in various areas of theoretical and applied physics. The main focus of this research centers on several key areas. First, infinitesimal generators of symmetries were found by Lie symmetry invariance analysis. Then, using the adjoint representation, an ideal system was created based on the found Lie vectors. Secondly, by utilizing the analytical approach, namely the modified Sardar sub equation method, we systematically derive various novel soliton solution in the form of dark, bright, periodic, singular, combo, hyperbolic as well as mixed trigonometric. Finally, bifurcation analysis is performed at the system’s fixed points, revealing chaotic behavior when an external force is introduced into the dynamic system. To identify the chaotic characteristics, a range of tools, such as 3D and 2D phase plots, time series, Lyapunov exponents, and multistability analysis, are utilized. Additionally, the sensitivity analysis of the model is examined under different initial conditions. These results enhance the understanding of nonlinear wave phenomena in mathematical physics and hold potential applications across numerous scientific disciplines.
期刊介绍:
Optical and Quantum Electronics provides an international forum for the publication of original research papers, tutorial reviews and letters in such fields as optical physics, optical engineering and optoelectronics. Special issues are published on topics of current interest.
Optical and Quantum Electronics is published monthly. It is concerned with the technology and physics of optical systems, components and devices, i.e., with topics such as: optical fibres; semiconductor lasers and LEDs; light detection and imaging devices; nanophotonics; photonic integration and optoelectronic integrated circuits; silicon photonics; displays; optical communications from devices to systems; materials for photonics (e.g. semiconductors, glasses, graphene); the physics and simulation of optical devices and systems; nanotechnologies in photonics (including engineered nano-structures such as photonic crystals, sub-wavelength photonic structures, metamaterials, and plasmonics); advanced quantum and optoelectronic applications (e.g. quantum computing, memory and communications, quantum sensing and quantum dots); photonic sensors and bio-sensors; Terahertz phenomena; non-linear optics and ultrafast phenomena; green photonics.