Symmetry Reductions of UT+U3UX +αUXXX X+βUY Y=0

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2019 by IJMTT Journal
Volume-65 Issue-6
Year of Publication : 2019
Authors : J. K. Subashini , B. Mayil Vaganan
  10.14445/22315373/IJMTT-V65I6P510

MLA

MLA Style:J. K. Subashini , B. Mayil Vaganan "Symmetry Reductions of UT+U3UX +αUXXX X+βUY Y=0" International Journal of Mathematics Trends and Technology 65.6 (2019): 61-66.

APA Style: J. K. Subashini , B. Mayil Vaganan (2019). Symmetry Reductions of UT+U3UX +αUXXX X+βUY Y=0 International Journal of Mathematics Trends and Technology, 61-66.

Abstract
A (2+1)-dimensional generalized KdV equation (ut+u3ux+αuxxx)x+βuyy =0, α, β∈ R+ is subjected to Lie’s classical method. Classification of its symmetry algebra into one- and two-dimensional subalgebras is carried out in order to facilitate its systematic reduction to (1+1) dimensional PDE and then to ODEs. A solution containing two arbitrary functions of time t is also determined.

Reference
[1] Ahmad, A., Ashfaque H. Bokhari., Kara, A.H., Zaman, F.D Symmetry classifications and reductions of some classes of (2+1)-nonlinear heat equation, J. Math. Anal. Appl., 339: 175-181 (2008).
[2] Bluman, G. W. and Kumei, S., Symmetries and Differential Equations, Springer-Verlag, New York, 1989. Liu Z. and Yang C.,The application of bifurcation method to a higher-order KdV equation, J. Math. Anal. Appl., 275: 1-12 (2002).
[3] Miura, R.M., Korteweg-de Vries equations and generalizations. A remarkable explicit nonlinear transformation, I.Math. Phys. 9: 1202-1204 (1968).
[4] Olver, P. J., Applications of Lie Groups to differential equations, Graduate Texts in Mathematics, 107, Springer-Verlag, New York, 1986.
[5] Senthilkumaran, M., Pandiaraja, D. and Mayil Vaganan, B. New Exact explicit Solutions of the Generalized KdV Equations 2008 Appl. Math. comp. 202 693-699
[6] Whitham, G. B., Linear and Nonlinear Waves, Wiley, New York, 1974.

Keywords
A (2+1)-dimensional generalized KdV equation; Symmetry algebra.