Note on Lie Point Symmetries of Burgers Equations
DOI:
https://doi.org/10.5540/tema.2010.011.02.0151Abstract
Abstract. In this note we study the Lie point symmetries of a class of evolution equations and obtain a group classification of these equations. We also identify the classical Lie algebras that the symmetry Lie algebras are isomorphic to.References
[1] G.W. Bluman, Simplifying the form of Lie groups admitted by a given differential equation, J. Math. Anal. Appl., 145 (1990), 52–62.
[2] G.W. Bluman, S. Kumei, “Symmetries and differential equations”, Applied Mathematical Sciences 81, Springer, 1989.
[3] Y.D. Bozhkov, Divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities, J. Diff. Equ., 225 (2006), 666–684.
[4] Y.D. Bozhkov, I.L. Freire, Group Classification of Semilinear Kohn-Laplace Equations, Nonlinear Anal., 68 (2008), 2552–2568.
[5] Y.D. Bozhkov, I.L. Freire, Conservations laws for critical Kohn-Laplace equations on the Heisenberg Group, J. Nonlinear Math. Phys., 15 (2008), 35–47.
[6] S. Dimas, D. Tsoubelis, SYM: A new symmetry-finding package for Mathematica, in “10th International Conference in Modern Group Analysis”, 64–70, 2005.
[7] S. Dimas, D. Tsoubelis, A new heuristic algorithm for solving overdetermined systems of PDEs in Mathematica, in “6th International Conference in Nonlinear Mathematical Physics”, 20–26, 2005.
[8] I.L. Freire, Note on Lie point symmetries of Burgers Equations, Anais do CNMAC, 2, (2009).
[9] N.H. Ibragimov, “Transformation groups applied to mathematical physics”, Translated from the Russian Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, 1985.
[10] V.I. Lagno, A.M. Samoilenko, Group classification of nonlinear evolution equations. I. Invariance under semisimple local transformation groups, Differ. Equ. 38 (2002), 384–391.
[11] M. Nadjafikhah, Lie symmetries of inviscid Burgers’ equation, Adv. Appl. Clif-ford Alg., 19 (2009), 101–112.
[12] P.J. Olver, “Applications of Lie groups to differential equations”, GMT 107, Springer, New York, 1986.
[13] A. Ouhadan, E.H. El Kinani, Lie symmetries of the equation ut(x, t) + g(u)ux(x, t) = 0, Adv. Appl. Clifford Alg., 17 (2007), 95–106.
[14] J. Patera, R.T. Sharp, P. Winternitz, H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Math. Phys., 17 (1976), 986–994.
[15] J. Patera, P. Winternitz, Subalgebras of real three- and four-dimensional Lie algebras, J. Math. Phys., 18 (1977), 1449–1455.
[16] R.O. Popovych, N.M. Ivanova, New results on group classification of nonlinear diffusion-convection equations, J. Phys. A: Math. Gen., 37 (2004), 7547–7565.
[17] S.R. Svirshchevskii, Group classification and invariant solutions of nonlinear polyharmonic equations, Differ. Equ./Diff. Uravn., 29 (1993), 1538–1547.
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