Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation

被引：40

作者：

Bozhkov, Yuri ^{[1
]}

Freire, Igor Leite ^{[1
,2
]}

机构：

[1] Univ Estadual Campinas, IMECC, BR-13083970 Campinas, SP, Brazil

[2] Univ Fed ABC UFABC, Ctr Matemat Comp & Cognicao, BR-09090400 Santo Andre, SP, Brazil

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2010年 / 249卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

Lie point symmetry; Noether symmetry; Conservation laws; Conformal group; PARTIAL-DIFFERENTIAL-EQUATIONS; DIRECT CONSTRUCTION METHOD; CONSERVATION-LAWS; GROUP CLASSIFICATION; WAVE-EQUATION; SURFACES;

D O I：

10.1016/j.jde.2010.04.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation laws. It is shown that the projection of the Lie point symmetries on M are special subgroups of the conformal group of M. In particular, if the scalar curvature of M vanishes, the projection on M of the Lie point symmetry group of the Poisson equation with critical nonlinearity is the conformal group of the manifold. We illustrate our results by applying them to the Thurston geometries. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：872 / 913

页数：42

共 31 条

[21] Polynomial and non-polynomial solutions set for wave equation using Lie point symmetries [J].

Lashkarian, Elham ;

Hejazi, S. Reza .

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2016, 4 (04) :298-308

[22] Lie point symmetries, conservation laws, and solutions of a space dependent reaction-diffusion equation [J].

Cao, Zhijie ;

Lin, Yiping .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 248 :386-398

[23] The (2+1)-dimensional time-fractional Kundu-Mukherjee-Naskar equation: Lie point symmetries, exact solutions and conservation laws [J].

Ling, Tao ;

Wang, Hui ;

Wang, Yunhu .

CHINESE JOURNAL OF PHYSICS, 2025, 96 :700-715

[24] Lie point symmetries, conservation laws and exact solutions of (1+n)-dimensional modified Zakharov-Kuznetsov equation describing the waves in plasma physics [J].

Ali, Muhammad Nasir ;

Seadawy, Aly R. ;

Husnine, Syed Muhammad .

PRAMANA-JOURNAL OF PHYSICS, 2018, 91 (04)

[25] Lie symmetries, exact wave solutions and conservation laws of nonlinear Bogovalenskii Breaking-Soliton equation for Nerve pulse propagation [J].

Kumar M. ;

Anand S. .

International Journal of Applied and Computational Mathematics, 2024, 10 (1)

[26] Exact and numerical solutions of time-fractional advection-diffusion equation with a nonlinear source term by means of the Lie symmetries [J].

Jannelli, Alessandra ;

Ruggieri, Marianna ;

Speciale, Maria Paola .

NONLINEAR DYNAMICS, 2018, 92 (02) :543-555

[27] Lie point symmetries and similarity solutions of the time-dependent coefficients Calogero-Degasperis equation [J].

Bansal, Anupma ;

Gupta, R. K. .

PHYSICA SCRIPTA, 2012, 86 (03)

[28] Lie point symmetries exact solutions and conservation laws of perturbed Zakharov-Kuznetsov equation with higher-order dispersion term [J].

Ali, Muhammad Nasir ;

Seadawy, Aly R. ;

Husnine, Syed Muhammad .

MODERN PHYSICS LETTERS A, 2019, 34 (03)

[29] ANALYSIS OF (1+n)-DIMENSIONAL GENERALIZED CAMASSA-HOLM KADOMTSEV-PETVIASHVILI EQUATION THROUGH LIE SYMMETRIES, NONLINEAR SELF-ADJOINT CLASSIFICATION AND TRAVELLING WAVE SOLUTIONS [J].

Hussain, Amjad ;

Jhangeer, Adil ;

Zia, Muhammad khubaib ;

Khan, Ilyas ;

Ganie, Abdul hamid ;

Eldin, Sayed m. .

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2023, 31 (10)

[30] Anisotropic non-linear time-fractional diffusion equation with a source term: Classification via Lie point symmetries, analytic solutions and numerical simulation [J].

Hejazi, S. Reza ;

Saberi, Elaheh ;

Mohammadizadeh, Fatemeh .

APPLIED MATHEMATICS AND COMPUTATION, 2021, 391 (391)

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