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Journal articles on the topic 'Lie symmetries'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Leach, P. G. L. "Lie symmetries and Noether symmetries." Applicable Analysis and Discrete Mathematics 6, no. 2 (2012): 238–46. http://dx.doi.org/10.2298/aadm120625015l.

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We demonstrate that so-called nonnoetherian symmetries with which a known first integral is associated of a differential equation derived from a Lagrangian are in fact noetherian. The source of the misunderstanding lies in the nonuniqueness of the Lagrangian.

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2

Nucci, M. C. "Lie symmetries of a Painlevé-type equation without Lie symmetries." Journal of Nonlinear Mathematical Physics 15, no. 2 (2008): 205–11. http://dx.doi.org/10.2991/jnmp.2008.15.2.7.

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3

Catuogno, Pedro José, and Luis Roberto Lucinger. "Random Lie-point symmetries." Journal of Nonlinear Mathematical Physics 21, no. 2 (2014): 149–65. http://dx.doi.org/10.1080/14029251.2014.900984.

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4

Nucci, M. C., and S. Post. "Lie symmetries and superintegrability." Journal of Physics A: Mathematical and Theoretical 45, no. 48 (2012): 482001. http://dx.doi.org/10.1088/1751-8113/45/48/482001.

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5

Sen, Tanaji. "Lie symmetries and integrability." Physics Letters A 122, no. 6-7 (1987): 327–30. http://dx.doi.org/10.1016/0375-9601(87)90835-8.

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6

Asghar, Nimra Sher, Kinza Iftikhar, and Tooba Feroze. "The Mei Symmetries for the Lagrangian Corresponding to the Schwarzschild Metric and the Kerr Black Hole Metric." Symmetry 14, no. 10 (2022): 2079. http://dx.doi.org/10.3390/sym14102079.

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In this paper, the Mei symmetries for the Lagrangians corresponding to the spherically and axially symmetric metrics are investigated. For this purpose, the Schwarzschild and Kerr black hole metrics are considered. Using the Mei symmetries criterion, we obtained four Mei symmetries for the Lagrangian of Schwarzschild and Kerr black hole metrics. The results reveal that, in the case of the Schwarzschild metric, the obtained Mei symmetries are a subset of the Lie point symmetries of equations of motion (geodesic equations), while in the case of the Kerr black hole metric, the Noether symmetry se

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7

Wang, Jianping, Huijing Ba, Yaru Liu, Longqi He, and Lina Ji. "Second-Order Conditional Lie-Bäcklund Symmetry and Differential Constraint of Radially Symmetric Diffusion System." Advances in Mathematical Physics 2021 (January 15, 2021): 1–17. http://dx.doi.org/10.1155/2021/8891750.

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The classifications and reductions of radially symmetric diffusion system are studied due to the conditional Lie-Bäcklund symmetry method. We obtain the invariant condition, which is the so-called determining system and under which the radially symmetric diffusion system admits second-order conditional Lie-Bäcklund symmetries. The governing systems and the admitted second-order conditional Lie-Bäcklund symmetries are identified by solving the nonlinear determining system. Exact solutions of the resulting systems are constructed due to the compatibility of the original system and the admitted d

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8

Nikitin, Anatolii. "Non-Lie Symmetries and Supersymmetries." Journal of Nonlinear Mathematical Physics 2, no. 3-4 (1995): 405–15. http://dx.doi.org/10.2991/jnmp.1995.2.3-4.21.

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9

Gazizov, Rafail K. "Lie Algebras of Approximate Symmetries." Journal of Nonlinear Mathematical Physics 3, no. 1-2 (1996): 96–101. http://dx.doi.org/10.2991/jnmp.1996.3.1-2.9.

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10

Tempesta, P. "Lie Symmetries and Weak Transversality." Theoretical and Mathematical Physics 137, no. 2 (2003): 1609–21. http://dx.doi.org/10.1023/a:1027326322183.

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11

Msomi, A. M., K. S. Govinder, and S. D. Maharaj. "Gravitating fluids with Lie symmetries." Journal of Physics A: Mathematical and Theoretical 43, no. 28 (2010): 285203. http://dx.doi.org/10.1088/1751-8113/43/28/285203.

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12

Charalambous, K., and PGL Leach. "Financial derivatives and Lie symmetries." Transactions of the Royal Society of South Africa 70, no. 1 (2014): 1–7. http://dx.doi.org/10.1080/0035919x.2014.945985.

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13

Merker, Joël. "Lie symmetries and CR geometry." Journal of Mathematical Sciences 154, no. 6 (2008): 817–922. http://dx.doi.org/10.1007/s10958-008-9201-5.

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14

Freire, Emilio, Armengol Gasull, and Antoni Guillamon. "Limit cycles and Lie symmetries." Bulletin des Sciences Mathématiques 131, no. 6 (2007): 501–17. http://dx.doi.org/10.1016/j.bulsci.2006.03.015.

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15

Song, Xu-Xia. "Lie Symmetries of Ishimori Equation." Communications in Theoretical Physics 59, no. 3 (2013): 253–56. http://dx.doi.org/10.1088/0253-6102/59/3/01.

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16

Sukhov, Alexandre. "Segre varieties and Lie symmetries." Mathematische Zeitschrift 238, no. 3 (2001): 483–92. http://dx.doi.org/10.1007/s002090100262.

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17

Duarte, L. G. S., L. A. C. P. da Mota, and A. F. Rocha. "Finding nonlocal Lie symmetries algorithmically." Chaos, Solitons & Fractals 177 (December 2023): 114232. http://dx.doi.org/10.1016/j.chaos.2023.114232.

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18

Paliathanasis, Andronikos, and Peter G. L. Leach. "Lie Symmetry Analysis of the Aw–Rascle–Zhang Model for Traffic State Estimation." Mathematics 11, no. 1 (2022): 81. http://dx.doi.org/10.3390/math11010081.

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We extend our analysis on the Lie symmetries in fluid dynamics to the case of macroscopic traffic estimation models. In particular we study the Aw–Rascle–Zhang model for traffic estimation, which consists of two hyperbolic first-order partial differential equations. The Lie symmetries, the one-dimensional optimal system and the corresponding Lie invariants are determined. Specifically, we find that the admitted Lie symmetries form the four-dimensional Lie algebra A4,12. The resulting one-dimensional optimal system is consisted by seven one-dimensional Lie algebras. Finally, we apply the Lie sy

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19

Paliathanasis, Andronikos. "Similarity Transformations and Linearization for a Family of Dispersionless Integrable PDEs." Symmetry 14, no. 8 (2022): 1603. http://dx.doi.org/10.3390/sym14081603.

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We apply the theory of Lie point symmetries for the study of a family of partial differential equations which are integrable by the hyperbolic reductions method and are reduced to members of the Painlevé transcendents. The main results of this study are that from the application of the similarity transformations provided by the Lie point symmetries, all the members of the family of the partial differential equations are reduced to second-order differential equations, which are maximal symmetric and can be linearized.

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20

Biswas, Indranil, and Niels Leth Gammelgaard. "Vassiliev invariants from symmetric spaces." Journal of Knot Theory and Its Ramifications 25, no. 10 (2016): 1650055. http://dx.doi.org/10.1142/s0218216516500553.

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We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are exactly characterized by having the symmetries of the Riemann curvature tensor.

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21

Paliathanasis, A., M. Tsamparlis, and M. T. Mustafa. "Symmetry analysis of the Klein–Gordon equation in Bianchi I spacetimes." International Journal of Geometric Methods in Modern Physics 12, no. 03 (2015): 1550033. http://dx.doi.org/10.1142/s0219887815500334.

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In this work we perform the symmetry classification of the Klein–Gordon equation in Bianchi I spacetime. We apply a geometric method which relates the Lie symmetries of the Klein–Gordon equation with the conformal algebra of the underlying geometry. Furthermore, we prove that the Lie symmetries which follow from the conformal algebra are also Noether symmetries for the Klein–Gordon equation. We use these results in order to determine all the potentials in which the Klein–Gordon admits Lie and Noether symmetries. Due to the large number of cases and for easy reference the results are presented

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22

Nadjafikhah, Mehdi, and Fatemeh Ahangari. "SYMMETRY ANALYSIS AND SIMILARITY REDUCTION OF THE KORTEWEG–DE VRIES–ZAKHAROV–KUZNETSOV EQUATION." Asian-European Journal of Mathematics 05, no. 01 (2012): 1250006. http://dx.doi.org/10.1142/s1793557112500064.

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In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system in mathematical physics, the Korteweg–de Vries–Zakharov–Kuznetsov (KdV–ZK) equation, is studied. By applying the basic Lie symmetry method for the KdV–ZK equation, the classical Lie point symmetry operators are obtained. Also, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The

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23

Bahamonde, Sebastian, Konstantinos Dialektopoulos, and Ugur Camci. "Exact Spherically Symmetric Solutions in Modified Gauss–Bonnet Gravity from Noether Symmetry Approach." Symmetry 12, no. 1 (2020): 68. http://dx.doi.org/10.3390/sym12010068.

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It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish those models of f ( R , G ) theory, with R and G being the Ricci and the Gauss–Bonnet scalars respectively, that are invariant under point transformations in a spherically symmetric background. In total, we find ten different forms of f that present symmetries and calculate their invariant quantities, i.e., Noether vector fields. Furthermore, we use these Noeth

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24

Zhao, Weidong, Muhammad Mobeen Munir, Hajra Bashir, Daud Ahmad, and Muhammad Athar. "Lie symmetry analysis for generalized short pulse equation." Open Physics 20, no. 1 (2022): 1185–93. http://dx.doi.org/10.1515/phys-2022-0212.

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Abstract Lie symmetry analysis (LSA) is one of the most common, effective, and estimation-free methods to find the symmetries and solutions of the differential equations (DEs) by following an algorithm. This analysis leads to reduce the order of partial differential equations (PDEs). Many physical problems are converted into non-linear DEs and these DEs or system of DEs are then solved with several methods such as similarity methods, Lie Bäcklund transformation, and Lie group of transformations. LSA is suitable for providing the conservation laws corresponding to Lie point symmetries or Lie Bä

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25

Tsamparlis, Michael, and Aniekan Magnus Ukpong. "Lie Symmetries of the Wave Equation on the Sphere Using Geometry." Dynamics 4, no. 2 (2024): 322–36. http://dx.doi.org/10.3390/dynamics4020019.

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A semilinear quadratic equation of the form Aij(x)uij=Bi(x,u)ui+F(x,u) defines a metric Aij; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets: one set containing the Lie derivative of the metric wrt the Lie symmetry generator, and the other set containing the quantities Bi(x,u),F(x,u). From the first set, it follows that the generators of Lie point symmetries are elements of the conformal algebra of the metric Aij, while the second set serves as constraint equations, which select ele

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26

Gui-zhang, T. "The Lie algebraic structure of symmetries generated by hereditary symmetries." Journal of Physics A: Mathematical and General 21, no. 9 (1988): 1951–57. http://dx.doi.org/10.1088/0305-4470/21/9/011.

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27

Paliathanasis, Andronikos, and Michael Tsamparlis. "The geometric origin of Lie point symmetries of the Schrödinger and the Klein–Gordon equations." International Journal of Geometric Methods in Modern Physics 11, no. 04 (2014): 1450037. http://dx.doi.org/10.1142/s0219887814500376.

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We determine the Lie point symmetries of the Schrödinger and the Klein–Gordon equations in a general Riemannian space. It is shown that these symmetries are related with the homothetic and the conformal algebra of the metric of the space, respectively. We consider the kinematic metric defined by the classical Lagrangian and show how the Lie point symmetries of the Schrödinger equation and the Klein–Gordon equation are related with the Noether point symmetries of this Lagrangian. The general results are applied to two practical problems: (a) The classification of all two- and three-dimensional

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28

Damers, Julien, Luc Jaulin, and Simon Rohou. "Lie symmetries applied to interval integration." Automatica 144 (October 2022): 110502. http://dx.doi.org/10.1016/j.automatica.2022.110502.

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29

Zhao, Weidong, Mobeen Munir, Ghulam Murtaza, and Muhammad Athar. "Lie symmetries of Benjamin-Ono equation." Mathematical Biosciences and Engineering 18, no. 6 (2021): 9496–510. http://dx.doi.org/10.3934/mbe.2021466.

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<abstract><p>Lie Symmetry analysis is often used to exploit the conservative laws of nature and solve or at least reduce the order of differential equation. One dimension internal waves are best described by Benjamin-Ono equation which is a nonlinear partial integro-differential equation. Present article focuses on the Lie symmetry analysis of this equation because of its importance. Lie symmetry analysis of this equation has been done but there are still some gaps and errors in the recent work. We claim that the symmetry algebra is of five dimensional. We reduce the model and solv

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30

Campoamor-Stursberg, Rutwig. "Lie-Point Symmetries Preserved by Derivative." Geometry Integrability and Quantization 21 (2020): 75–88. http://dx.doi.org/10.7546/giq-21-2020-75-88.

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31

Vaneeva, O. O., and A. Yu Zhalij. "Lie symmetries of generalized Kawahara equations." Reports of the National Academy of Sciences of Ukraine, no. 12 (December 2020): 3–10. http://dx.doi.org/10.15407/dopovidi2020.12.003.

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We carry out the group classification of a normalized class of generalized Kawahara equations with variable coefficients. Admissible transformations are studied, and the partition of the class into two normalized subclasses is performed. For each of these subclasses, the respective equivalence groupoids are found. As a result, all equations from the class admitting Lie symmetry extensions are revealed.

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32

Levi, D., S. Tremblay, and P. Winternitz. "Lie symmetries of multidimensional difference equations." Journal of Physics A: Mathematical and General 34, no. 44 (2001): 9507–24. http://dx.doi.org/10.1088/0305-4470/34/44/311.

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33

Ali, Sajid, Fazal M. Mahomed, and Asghar Qadir. "Complex Lie Symmetries for Variational Problems." Journal of Nonlinear Mathematical Physics 15, sup1 (2008): 25–35. http://dx.doi.org/10.2991/jnmp.2008.15.s1.2.

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34

Flessas, G. P., and P. G. L. Leach. "Riemann's equation and Lie point symmetries." Physica Scripta 73, no. 4 (2006): 377–83. http://dx.doi.org/10.1088/0031-8949/73/4/011.

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35

Beckers, J., N. Debergh, and A. G. Nikitin. "Lie extended symmetries and relativistic particles." Journal of Physics A: Mathematical and General 25, no. 22 (1992): 6145–54. http://dx.doi.org/10.1088/0305-4470/25/22/035.

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36

Sen, Tanaji, and M. Tabor. "Lie symmetries of the Lorenz model." Physica D: Nonlinear Phenomena 44, no. 3 (1990): 313–39. http://dx.doi.org/10.1016/0167-2789(90)90152-f.

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37

Tamizhmani, K. M., A. Ramani, and B. Grammaticos. "Lie symmetries of Hirota’s bilinear equations." Journal of Mathematical Physics 32, no. 10 (1991): 2635–59. http://dx.doi.org/10.1063/1.529506.

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38

Floreanini, Roberto, and Luc Vinet. "Lie symmetries of finite‐difference equations." Journal of Mathematical Physics 36, no. 12 (1995): 7024–42. http://dx.doi.org/10.1063/1.531205.

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39

Simoni, A., A. Stern, and I. Yakushin. "Lorentz transformations as Lie–Poisson symmetries." Journal of Mathematical Physics 36, no. 10 (1995): 5588–97. http://dx.doi.org/10.1063/1.531278.

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40

Shi Shen-Yang, Fu Jing-Li, and Chen Li-Qun. "Lie symmetries of discrete Lagrange systems." Acta Physica Sinica 56, no. 6 (2007): 3060. http://dx.doi.org/10.7498/aps.56.3060.

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41

Kalnins, E. G., and Willard Miller, Jr. "Related Evolution Equations and Lie Symmetries." SIAM Journal on Mathematical Analysis 16, no. 2 (1985): 221–32. http://dx.doi.org/10.1137/0516017.

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42

Levi, Decio, and Miguel A. Rodríguez. "Lie discrete symmetries of lattice equations." Journal of Physics A: Mathematical and General 37, no. 5 (2004): 1711–25. http://dx.doi.org/10.1088/0305-4470/37/5/016.

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43

Cicogna, G., and G. Gaeta. "On Lie point symmetries in mechanics." Il Nuovo Cimento B Series 11 107, no. 9 (1992): 1085–96. http://dx.doi.org/10.1007/bf02727046.

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44

Leach, P. G. L. "Heat polynomials and Lie point symmetries." Journal of Mathematical Analysis and Applications 322, no. 1 (2006): 288–97. http://dx.doi.org/10.1016/j.jmaa.2005.09.025.

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45

Cicogna, G., and G. Gaeta. "Nonlinear Lie symmetries in bifurcation theory." Physics Letters A 172, no. 5 (1993): 361–64. http://dx.doi.org/10.1016/0375-9601(93)90118-j.

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46

Cho, Dai-Ning, and Otto C. W. Kong. "Relativity symmetries and Lie algebra contractions." Annals of Physics 351 (December 2014): 275–89. http://dx.doi.org/10.1016/j.aop.2014.09.005.

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47

Nadjafikhah, Mehdi. "Lie Symmetries of Inviscid Burgers’ Equation." Advances in Applied Clifford Algebras 19, no. 1 (2008): 101–12. http://dx.doi.org/10.1007/s00006-008-0127-2.

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48

MARMO, G., A. SIMONI, and A. STERN. "POISSON LIE GROUP SYMMETRIES FOR THE ISOTROPIC ROTATOR." International Journal of Modern Physics A 10, no. 01 (1995): 99–114. http://dx.doi.org/10.1142/s0217751x9500005x.

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We find a new Hamiltonian formulation of the classical isotropic rotator where left and right SU(2) transformations are not canonical symmetries but rather Poisson Lie group symmetries. The system corresponds to the classical analog of a quantum-mechanical rotator which possesses quantum group symmetries. We also examine systems of two classical interacting rotators having Poisson Lie group symmetries.

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49

Yang, Hongwei, Yunlong Shi, Baoshu Yin, and Huanhe Dong. "Discrete Symmetries Analysis and Exact Solutions of the Inviscid Burgers Equation." Discrete Dynamics in Nature and Society 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/908975.

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We discuss the Lie point symmetries and discrete symmetries of the inviscid Burgers equation. By employing the Lie group method of infinitesimal transformations, symmetry reductions and similarity solutions of the governing equation are given. Based on discrete symmetries analysis, two groups of discrete symmetries are obtained, which lead to new exact solutions of the inviscid Burgers equation.

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50

Paliathanasis, Andronikos. "Projective Collineations of Decomposable Spacetimes Generated by the Lie Point Symmetries of Geodesic Equations." Symmetry 13, no. 6 (2021): 1018. http://dx.doi.org/10.3390/sym13061018.

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We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations. In this study, we prove that the projective collineations of a n+1-dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the n-dimensional subspace. We demonstrate the application of our results with the presenta

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