The Lie group method is used in order to investigate various issues related to symmetries and exact solutions of the barotropic vorticity equation. This is done in a similar but more systematic and complete way as given by Huang and Lou [Phys. Lett. A. 320 (2004) 428–437]. The Lie symmetries of the barotropic vorticity equations on the f and β-planes as well as on the sphere in rotating and res...

For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the normal form method, center manifold theory, and the renormalization group method are well known. It is shown that all of the solutions of the reduced equatio...

Lie transformation groups containing a one-dimensional subgroup acting cyclically on a manifold are considered. The structure of the group is found to be considerably restricted by the existence of a one-dimensional subgroup whose orbits are circles. The results proved do not depend on the dimension of the manifold nor on the existence of a metric, but merely on the fact that the Lie group acts...

In the present paper, the Sawada–Kotera equation is considered by Lie symmetry analysis. All of the geometric vector fields to the Sawada–Kotera equation are obtained, and then the symmetry reductions and exact solutions of the Sawada–Kotera equation are investigated. Our results show that symmetry analysis is a very efficient and powerful technique in finding the solution of the proposed equat...

The boundary layer problem for power-law fluid can be recast to a third-order p-Laplacian boundary value problem (BVP). In this paper, we transform the third-order p-Laplacian into a new system which exhibits a Lie-symmetry SL(3,R). Then, the closure property of the Lie-group is used to derive a linear transformation between the boundary values at two ends of a spatial interval. Hence, we can i...

In present paper, the Sharma-Tasso-Olever (STO) equation is considered by the Lie symmetry analysis. All of the geometric vector fields to the STO equation are obtained, then the symmetry reductions and exact solutions of the STO equation are investigated. Our results witness that symmetry analysis was very efficient and powerful technique in finding the solutions of the proposed equation.