Symmetry group classification for general Burgers' equation

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 9, 2010, Pages 2303-2310

  Nadjafikhah, M ^a   Bakhshandeh Chamazkoti, R ^a  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

General Burgers' equation; Infinitesimal generator; Optimal system; Preliminarily group classification

Indexed keywords

ALGEBRA;

ADJOINT REPRESENTATION; ALGEBRAIC APPROACHES; BURGER'S EQUATIONS; GENERAL BURGER' EQUATION; GROUP CLASSIFICATION; INFINITESIMAL GENERATOR; LIE ALGEBRA; PRELIMINARILY GROUP CLASSIFICATION; SMOOTH FUNCTIONS; SYMMETRY GROUPS;

OPTIMAL SYSTEMS;

EID: 77949655430     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.09.031     Document Type: Article

References (17)

1. Lie S. On integration of a class of linear partial differential equations by means of definite integrals. Arch Math 6 (1881) 328 Translation by Ibragimov NH
2. Ovsiannikov L.V. Group analysis of differential equations (1982), Academic Press, New York
3. x). J Math Phys 32 11 (1991) 2988-2995
4. xx + g (x, u). Nonlinear Anal (2008) 10.1016/j.na.2008.07.008
5. x). Commun Nonlinear Sci Numer Simul 9 (2004) 6980
6. Gardner C.S., Greene J.M., Kruskal M.D., and Miura R.M. Method for solving the Kortewegde Vries equation. Phys Rev Lett 19 (1967) 10951097
7. Li Y.S. Soliton and integrable systems. Advanced series in nonlinear science (1999), Shanghai Scientific and Technological Education Publishing House, Shang Hai [in Chinese]
8. Hirota R., and Satsuma J. A variety of nonlinear network equations generated from the Bäcklund transformation for the Tota lattice. Suppl Prog Theor Phys 59 (1976) 64100
9. Olver P.J. Applications of Lie group to differential equations. Graduate text maths vol. 107 (1986), Springer, New York
10. Bluman G.W., and Kumei S. Symmetries and differential equations (1989), SpringerVerlag, World Publishing Corp.
11. Cantwell B.J. Introduction to symmetry analysis (2002), Cambridge University Press
12. Liu H., Li J., and Zhangb Q. Lie symmetry analysis and exact explicit solutions for general Burgers' equation. J Comput Appl Math (2008) 10.1016/j.cam. 2008.06.009
13. Gandarias M.L., Torrisi M., and Tracina R. On some differential invariants for a family of diffusion equations. J Phys A: Math Theor 40 (2007) 8803-8813
14. Torrisi M., and Tracina R. Second-order differential invariants of a family of diffusion equations. J Phys A: Math Gen 38 (2005) 7519-7526
15. Gandarias M.L., Torrisi M., and Valenti A. Symmetry classification and optimal systems of a non-linear wave equation. Int J Nonlinear Mech 39 (2004) 389398
16. Maluleke G.H., and Mason D.P. Optimal system and group invariant solutions for a nonlinear wave equation. Commun Nonlinear Sci Numer Simul 9 (2004) 93104
17. Olver P.J. Equivalence, invariants, and symmetry (1995), Cambridge University Press, Cambridge