SAMS Subject Classification Number: 3

In this talk, we perform Lie group analysis [1–5] on a third-order non-linear partial differential equation, namely potential Kortweg-de Vries equation [6]. We first compute Lie symmetries and then perform symmetry reductions on it. Thereafter, we use the direct integration method to obtain its travelling wave solutions. Furthermore, conserved vectors for this equation are derived using the multiplier method [7] and the theorem due to Ibragimov [8].
[1] L.V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York, 1982

[2] G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer- Verlag, New York, 1989

[3] N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Vols 1-3, CRC Press, Boca Raton, Florida, 1994-1996

[4] N.H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley & Sons, Chichester, NY, 1999

[5] G.W. Bluman, A.F. Cheviakov, S.C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer, New York, 2010

[6] A.M. Wazwaz, S.A. El-Tantawy, A new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, Nonlinear Dyn., 84 (2016) 1107–1112

[7] P.J. Olver, Applications of Lie Groups to Differential Equations, second ed., Springer-Verlag, Berlin, 1993

[8] N H. Ibragimov, A new conservation theorem. Journal of Mathematical Analysis and Applications, 333(1), ( 2007) 311–328