Stellenbosch University
Lie group classification of a variable coefficients
Gardner equation
Tanki Motsepa\(^*\), School of Computing and
Mathematical Sciences, University of Mpumalanga
Chaudry Masood Khalique, International
Institute for Symmetry Analysis and Mathematical Modelling, North-West
University
SAMS Subject Classification Number: 3
In this talk, we perform Lie group classification of a variable coefficients Gardner equation [1], which describes various interesting physics phenomena, such as the internal waves in a stratified ocean, the long wave propagation in an inhomogeneous two-layer shallow liquid and ion acoustic waves in plasma with a negative ion. The Lie group classification [2] of the equation provides us with four-dimensional equivalence Lie algebra and has several possible extensions. It is further shown that several cases arise in classifying the arbitrary parameters. Finally, conservation laws are obtained for certain cases using the multiplier approach [3].
References
[1] Hong, B., Lu, D., New exact solutions for the generalized variable-coefficient Gardner equation with forcing term. Applied Mathematics and Computation, 219, pp.2732–2738.
[2] Olver, P.J., 2000. Applications of Lie groups to differential equations (Vol. 107). Springer Science & Business Media.
[3] Bluman, G.W., Cheviakov, A.F., Anco, S.C., 2010. Applications of Symmetry Methods to Partial Differential Equations (Vol. 168). Springer.
