SAMS Subject Classification Number: 3

In this talk, the 2D new extended Kadomtsev–Petviashvili equation [1] is considered and analysed using the Lie symmetry analysis technique [2]. Firstly, Lie point symmetries are obtained and used to derive some exact solutions of this model. Moreover symmetry reductions result in several nonlinear ordinary differential equations, which we solve with the aid of Kudryashov’s and the simplest equation method. Furthermore we compute the conserved vectors of the underlying equation using the direct method [3].

[1] Y.L. Ma, A.M. Wazwaz, B.Q. Li, A new \((3+1)\)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves., Mathematics and computers in simulation, 187 (2021) 505–519.

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

[3] S.C. Anco, G. Bluman, Direct construction method for conservation laws of partial differential equations part 1, Euro. Jnl of Applied Mathematics, 13 (2002) 545-566.