Symmetry Classifications and Reductions of (2+1)- Dimensional Korteweg-de Vries Equation
Keywords:
Korteweg-de Vries Equation, Symmetry algebra
Abstract
We establish the symmetry reductions of (2+1)- Dimensional Korteweg-de Vries Equation, (ut + u + u3ux + αuxxx)x + βuyy = 0 is subjected to the Lie’s classical method. Classification of its symmetry algebra into one- and two-dimensional subalgebras are carried out in order to facilitate its reduction systematically to (1+1)-dimensional PDEs and then to first or second-order ODEs.
References
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P.J.Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, (1986).
A.Ahmad, Ashfaque H.Bokhari, A.H.Kara and F.D.Zaman, Symmetry Classifications and Reductions of Some Classes of (2+1)-Nonlinear Heat Equation, J. Math. Anal. Appl., 339(2008), 175-181.
Z.Liu and C.Yang ,The application of bifurcation method to a higher-order KdV equation, J. Math. Anal. Appl., 275(2002), 1-12.
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P.J.Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, (1986).
A.Ahmad, Ashfaque H.Bokhari, A.H.Kara and F.D.Zaman, Symmetry Classifications and Reductions of Some Classes of (2+1)-Nonlinear Heat Equation, J. Math. Anal. Appl., 339(2008), 175-181.
Z.Liu and C.Yang ,The application of bifurcation method to a higher-order KdV equation, J. Math. Anal. Appl., 275(2002), 1-12.
R.M.Miura, Korteweg-de Vries equations and generalizations. A remarkable explicit nonlinear transformation, I.Math. Phys., 9(1968), 1202-1204.
D.J.Korteweg and G.de Vries, On the Chans of Form of Long Waves Advancing in a Rectangular canal, and On a New type of Long Stationary Waves, Philosophical Magazine, 39(1985), 422-443.
F.Gungor and P.Winternitz, Generalized Kadomtsev Petviashvili equation with an infinitesimal dimensional symmetry algebra, J. Math. Anal., 276(2002), 314-328.
F.Gungor and P.Winternitz, Equaivalence Classes and Symmetries of the Variable Coefficient Kadomtsev Petviashvili Equation, Nonlinear Dynamics, 35(2004), 381-396.
How to Cite
T.Siva Subramania Raja, S.Padmasekaran, R.Asokan, & G.Ramkumar. (2016). Symmetry Classifications and Reductions of (2+1)- Dimensional Korteweg-de Vries Equation. International Journal of Current Research in Science and Technology, 2(3), 1-10. Retrieved from https://crst.gfer.org/index.php/crst/article/view/65
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