检索结果-南通市图书馆

Birkhoff’s Theorem and lie symmetry analysis

在线全文

学校读者我要写书评

暂无评论

Journal of High Energy Physics, Gravitation and Cosmology 2021年第4期7卷 1280-1297页

作者： Avijit Mukherjee Subham B. Roy Relativity and Cosmology Research Centre Department of Physics Jadavpur University Jadavpur India Department of Physics University at Albany State University of New York New York US Formerly at Relativity and Cosmology Research Centre Department of Physics Jadavpur University Jadavpur India

Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einstein’s Field equations for vacuum, yields the Schwarzschild Metric as the unique solution, which essentially is the statement of the well known Birkhoff’s Theorem. Geometrically speaking this theorem claims that the pseudo-Riemanian space-times provide more isometries than expected from the original metric holonomy/ansatz. In this paper we use the method of lie symmetry analysis to analyze the Einstein’s Vacuum Field Equations so as to obtain the symmetry Generators of the corresponding Differential Equation. Additionally, applying the Noether Point symmetry method we have obtained the conserved quantities corresponding to the generators of the Schwarzschild Lagrangian and paving way to reformulate the Birkhoff’s Theorem from a different approach.

关键词： Birkhoff’s Theorem lie symmetry analysis Noether Point symmetry

Nonclassical lie symmetry and conservation laws of the nonlinear timefractional Korteweg–de Vries equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2021年第9期73卷 59-67页

作者： Mir Sajjad Hashemi Ali Haji-Badali Farzaneh Alizadeh Mustafa Inc Department of Mathematics Basic Science FacultyUniversity of BonabBonabBox 55513-95133Iran Department of Computer Engineering Biruni UniversityIstanbulTurkey Department of Mathematics Science FacultyFirat University23119 ElazigTurkey Department of Medical Research China Medical University HospitalChina Medical UniversityTaichungTaiwanChina

In this paper,we use the symmetry of the lie group analysis as one of the powerful tools that deals with the wide class of fractional order differential equations in the Riemann–Liouville *** this study,first,we employ the classical and nonclassical lie symmetries(LS)to acquire similarity reductions of the nonlinear fractional far field Korteweg–de Vries(KdV)equation,and second,we find the related exact solutions for the derived ***,according to the LS generators acquired,we construct conservation laws for related classical and nonclassical vector fields of the fractional far field KdV equation.

关键词： fractional equation lie symmetry analysis classical and non-classical symmetries

Conservation laws,lie symmetries,self adjointness,and soliton solutions for the Selkov–Schnakenberg system

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2024年第2期76卷 29-44页

作者： Kashif Ali Aly R Seadawy Syed T R Rizvi Noor Aziz Department of Mathematics COMSATS University IslamabadLahore CampusPakistan Mathematics Department Faculty of ScienceTaibah UniversityAl-Madinah Al-Munawarah41411Saudi Arabia

In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for lie symmetry analysis,self-adjointness,and conservation ***,miscellaneous soliton solutions like dark,bright,periodic,rational,Jacobian elliptic function,Weierstrass elliptic function,and hyperbolic solutions of the SS system will be achieved by a well-known technique called sub-ordinary differential *** these results are displayed graphically by 3D,2D,and contour plots.

关键词： Selkov-Schnakenberg system lie symmetry analysis conservation laws adjointness integrability

Conserved vectors and symmetry solutions of the Landau–Ginzburg–Higgs equation of theoretical physics

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2024年第4期76卷 51-65页

作者： Chaudry Masood Khalique Mduduzi Yolane Thabo Lephoko Material Science Innovation and Modelling Research Focus AreaDepartment of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X 2046Mmabatho 2735South Africa

This paper is devoted to the investigation of the Landau–Ginzburg–Higgs equation(LGHe),which serves as a mathematical model to understand phenomena such as superconductivity and cyclotron *** LGHe finds applications in various scientific fields,including fluid dynamics,plasma physics,biological systems,and *** study adopts lie symmetry analysis as the primary framework for *** analysis involves the identification of lie point symmetries that are admitted by the differential *** leveraging these lie point symmetries,symmetry reductions are performed,leading to the discovery of group invariant *** obtain explicit solutions,several mathematical methods are applied,including Kudryashov's method,the extended Jacobi elliptic function expansion method,the power series method,and the simplest equation *** methods yield solutions characterized by exponential,hyperbolic,and elliptic *** obtained solutions are visually represented through 3D,2D,and density plots,which effectively illustrate the nature of the *** plots depict various patterns,such as kink-shaped,singular kink-shaped,bell-shaped,and periodic ***,the paper employs the multiplier method and the conservation theorem introduced by Ibragimov to derive conserved *** conserved vectors play a crucial role in the study of physical quantities,such as the conservation of energy and momentum,and contribute to the understanding of the underlying physics of the system.

关键词： Landau-Ginzburg-Higgs equation lie symmetry analysis group invariant solutions conserved vectors multiplier method Ibragimov's method

Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via lie symmetry approach together with a couple of integration approaches

在线全文

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2023年第3期8卷 226-237页

作者： Shoukry El-Ganaini Sachin Kumar Monika Niwas Department of Mathematics Faculty of ScienceDamanhour UniversityDamanhour 22514Egypt Department of Mathematics Faculty of Mathematical SciencesUniversity of DelhiDelhi 110007India Department of Mathematics University of DelhiDelhi 110007India

By taking advantage of three different computational analytical methods:the lie symmetry analysis,the generalized Riccati equation mapping approach,and the modified Kudryashov approach,we construct multiple new analytical soliton solutions to the nonlinear convection-diffusion-reaction equation(NCDR)with power-law nonlinearity and density-dependent *** symmetry analysis is one of the pow-erful techniques that reduce the higher-order partial differential equation into an ordinary differential equation by reduction of independent *** the lie group technique,we obtain one-parameter in-variant transformations,determining equations and corresponding vectors for the considered convection-diffusion-reaction *** treating the parameters of the governing equation as constants,the ap-plied methods yield a variety of new closed-form solutions,including inverse function solutions,periodic solutions,exponential function solutions,dark solitons,singular solitons,combo bright-singular solitons,and the combine of bright-dark solitons and dark-bright ***,using the Bäcklund transfor-mation of the generalized Riccati equation and modified Kudryashov method,we can construct multiple solitons and other solutions of the considered *** obtained new solutions of this work demon-strate that the used approaches are powerful and effective in dealing with nonlinear equations,and that these solutions are required to explain many biological and physical *** our obtained solutions of this paper with the ones obtained in the literature,we see that our solutions are new and not reported *** newly formed soliton solutions will be more beneficial in the various dis-ciplines of ocean engineering,plasma physics,and nonlinear sciences.

关键词： lie symmetry analysis Generalized riccati equation mapping Modified kudryashov approach Nonlinear convection-diffusion-reaction equation Solitary wave solutions Closed form solutions Backlund transformation Exact solution Dynamical wave structures Bäcklund transformation

Symmetries,optimal system,exact and soliton solutions of(3+1)-dimensional Gardner-KP equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2024年第2期9卷 178-190页

作者： Amjad Hussain Ashreen Anjum M.Junaid-U-Rehman Ilyas Khan Mariam A.Sameh Amnah S.Al-Johani Department of Mathematics Quaid-I-Azam University 45320Islamabad 44000Pakistan Department of Mathematics College of Science Al-ZulfiMajmaah UniversityAl-MajmaahP.O Box 66Majmaah 11952Saudi Arabia Electrical Engineering Department Faculty of Engineering and TechnologyFuture University in EgyptNew Cairo 11845Egypt Mathematics Department Faculty of ScienceUniversity of TabukTabukSaudi Arabia

In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the lie group-theoretic *** the lie invariance condition,we find the symmetry *** pro-posed model yields eight-dimensional lie ***,an optimal system of sub-algebras is com-puted,and similarity reductions are *** considered nonlinear partial differential equation is re-duced into ordinary differential equations(ODEs)by utilizing the similarity transformation method(STM),which has the benefit of yielding a large number of accurate traveling wave *** ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases,while in other cases,we use the new auxiliary equation method to get its soliton *** evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.

关键词： Gardner-KP equation lie symmetry analysis Optimal system New auxiliary equation method Solitary wave solutions

Some New Nonlinear Wave Solutions for a Higher-Dimensional Shallow Water Wave Equation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Applied Mathematics and Physics 2020年第9期8卷 1845-1860页

作者： Longmin Dong Zhu Guo Yinghui He Department of Mathematics Honghe University Mengzi China

In this manuscript, we first perform a complete lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained lie symmetries. Moreover, with the extended F-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function.

关键词： Shallow Water Wave Equations Nonlinear Wave Solution lie symmetry analysis Extended F-Expansion Method

symmetry Reductions and Exact Solutions to the Variable-coefficients mKdV Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Symmetry Reductions and Exact Solutions to the Variable-coef...