Stellenbosch University
Conserved vectors and solutions of the
two-dimensional potential KP equation
Mduduzi Yolane Thabo Lephoko\(^*\), Chaudry Masood
Khalique,
International Institute for Symmetry Analysis and Mathematical
Modelling,
North-West University
SAMS Subject Classification Number: 3
In this talk, we study the potential Kadomtsev-Petviashvili equation [1] which has many applications in fields such as plasma physics, phase imaging and nonlinear mechanics. Using the technique of Lie symmetry analysis [2], we first compute its Lie point symmetries. Thereafter, group-invariant solutions are determined under each symmetry. Finally, conservation laws for this equation are derived using the conservation theorem due to Ibragimov [3].
References
[1] Ma, W.X., Manukure, S., Wang, H. and Batwa, S., 2021. Lump solutions to a (2+ 1)-dimensional fourth-order nonlinear PDE possessing a Hirota bilinear form. Modern Physics Letters B, 35(09), p.2150160.
[2] Olver, P.J., 2000. Applications of Lie groups to differential equations (Vol. 107). Springer Science & Business Media.
[3] Ibragimov, N.H., 2007. A new conservation theorem. Journal of Mathematical Analysis and Applications, 333(1), pp.311-328.
