Lie group symmetries and Riemann function of Klein–Gordon–Fock equation with central symmetry

Kochetov, Bogdan A.

doi:10.1016/j.cnsns.2013.10.001

Cited by 11 publications

(4 citation statements)

References 9 publications

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“…A symmetry of a system of differential equations is a transformation that maps any solution to another solution [5,13]. Such transformations are groups that depend on continuous parameters and consist of transformations (point symmetries), acting in the system space of independent and dependent variables, as well as in all the first derivatives of the dependent variables [14,15]. Elementary examples of Lie groups include: translations, rotations, and scaling [6,8].…”

Section: Introductionmentioning

confidence: 99%

Applications of the Lie symmetries to complete solution of a bead on a rotating wire hoop

Basquerotto

Righetto

Silva

2018

J Braz. Soc. Mech. Sci. Eng.

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The existence of Lie symmetries in differential equations can generate transformations in the dependent and independent variables and obtain new equations that may be easier to integrate. In particular, in some situations, one can reduce the order and it is possible to obtain first integrals. Thus, this article presents the application of the fundamental Lie theorem to obtain the complete solution of a classical nonlinear problem of the dynamics of mechanical systems: the bead on a rotating wire hoop. From the first integral obtained with the Lie symmetry generators, the exact solution can be found with the aid of the Jacobi elliptic functions.

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Section: Introductionmentioning

confidence: 99%

Applications of the Lie symmetries to complete solution of a bead on a rotating wire hoop

Basquerotto

Righetto

Silva

2018

J Braz. Soc. Mech. Sci. Eng.

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“…A key focus of our work is the derivation of evolutionary equations for electromagnetic fields in conical geometries, an essential step toward solving modal amplitudes in such structures. While the development of numerical techniques, particularly finite difference methods has been instrumental in advancing the field [20]- [26], our study primarily concentrates on the theoretical formulation of evolutionary equations in conical configurations using the novel format of Maxwell's equations [18]. Rather than presenting numerical solutions, our focus is on the conceptual and analytical framework that lays the groundwork for future numerical analyses and applications in complex electromagnetic scenarios.…”

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confidence: 99%

Time-Domain Analysis of Electromagnetic Fields in Conical Cavities With Modified EAE

Cosan,

Erden,

Aksoy

2024

IEEE Access

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In this study, we apply a novel format of Maxwell's equations in SI Units for analyzing electromagnetic fields in conical cavities, with a special focus on time-domain analysis. This unique approach aligns the dimensions of electric (E) and magnetic (H) fields as inverse meters, thereby facilitating theoretical investigations into complex geometrical field behaviors. Our primary focus is on deriving evolutionary equations for electromagnetic fields within conical structures. Additionally, this study serves as a stepping stone for future in-depth research into the mechanical properties of electromagnetic fields, particularly due to the unified dimensional approach of E and H fields. This method is expected to provide more insightful perspectives in understanding the dynamics of electromagnetic fields in conical cavities. The implications of this research extend to practical applications, notably in the design and analysis of microwave resonant cavities and conical antennas, enhancing our comprehension of electromagnetic phenomena in specialized structures within the broader scope of electrodynamics.INDEX TERMS Maxwell's equations, conical cavities, evolutionary electrodynamics, time domain.

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“…(1) occurs very often in phenomena in which central symmetry plays a key role, such as in certain quantum physical problems. Very recently, Kochetov [11] studied the Klein-Gordon-Fock equation with central symmetry using the classical Lie symmetry method. Later on, in [1] conservation laws for the same equation were established.…”

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confidence: 99%

“…Inspired by the works of [11,1] we study the following natural two-component extension of equation (1),…”

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confidence: 99%

Symmetry analysis of a Lane-Emden-Klein-Gordon-Fock system with central symmetry

Freire¹,

Muatjetjeja²

2018

Discrete &Amp; Continuous Dynamical Systems - S

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Lie group symmetries and Riemann function of Klein–Gordon–Fock equation with central symmetry

Cited by 11 publications

References 9 publications

Applications of the Lie symmetries to complete solution of a bead on a rotating wire hoop

Applications of the Lie symmetries to complete solution of a bead on a rotating wire hoop

Time-Domain Analysis of Electromagnetic Fields in Conical Cavities With Modified EAE

Symmetry analysis of a Lane-Emden-Klein-Gordon-Fock system with central symmetry

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