Stellenbosch University
Symmetry analysis and conservation laws of the Alice
Bob-KP equation
Bodibe Jonathan Lebogang\(^*\), Chaudry Masood
Khalique,
International Institute for Symmetry Analysis and Mathematical
Modelling,
Department of Mathematical Sciences, North-West University
SAMS Subject Classification Number: 3
In this talk, we study the nonlinear partial differential equation
(NLPDE), namely, the Alice Bob-KP equation [1] which has many
applications in fields such as dispersive media [2,3] and multicomponent
plasmas [4]. Using the technique of Lie symmetry analysis [5], Firstly,
we compute the Lie point symmetries of the Alice Bob-KP equation and
then perform symmetry reductions. Exact solutions are obtained.
Furthermore, conservation laws for this equation are derived using the
multiplier method [6].
References
[1] H.Y. Wu, J.X. Fei, Z.Y. Ma, J.C. Chen, W.X. Ma, Symmetry Breaking Soliton, Breather, and Lump Solutions of a Nonlocal Kadomtsev-Petviashvili System, Complexity (2020) 6423205, 13 pages
[2] M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, PA, USA, 1981.
[3] V. I. Petviashvili and O. V. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere, Energoatomizdat, Moscow, Russia, 1989.
[4] G. C. Das and J. Sarma, “Evolution of solitary waves in multicomponent plasmas,” Chaos, Solitons and Fractals, vol. 9, no. 6, pp. 901–911, 1998.
[5] N.H. Ibragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley and Sons, Chichester, NY,USA,1999.
[6] P.J. Olver, Applications of Lie Groups to Differential Equations, Springer-Verlag, New York, 1993.
