Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Li...

We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, non classical, Lie-Bäcklund and potential symmetries, invariant solutions, first-integrals, Nöther theorem for both discrete and continuous systems, solution of ordinary differential equa...

Since its introduction in 1980, the Kadomtsev-Petviashvili(KP) hierarchy [1, 2] is one of the most important research topics in the area of classical integrable systems. In particular, the study of its symmetries plays a central role in the development of this theory. In this context, additional symmetries, which correspond to a special kind of symmetries depending explicitly on the independent...

the purpose of this paper is to analyze in detail a special nonlinear partial differentialequation (npde) of the second order which is important in physical, chemical and technicalapplications. the present npde describes nonlinear diffusion and is of interest in several partsof physics, chemistry and engineering problems alike. since nature is not linear intrinsicallythe nonlinear case is there...

We are looking for the universal covering algebra for all symmetries of a given pde, using the sine-Gordon equation as a typical example for a non-evolution equation. For non-evolution equations, Estabrook-Wahlquist prolongation structures for non-local symmetries depend on the choice of a specific sub-ideal, of the contact module, to define the pde. For each inequivalent such choice we determi...

Lie group analysis is applied to a mathematical model for thin liquid films, namely nonlinear fourth order partial differential equation in two independent variables. A three-dimensional symmetry algebra found and reductions ordinary equations are obtained by using its one-dimensional subalgebras. Two of these studied the reduction method Jacobi last multiplier method, be linearizable. Furtherm...

‎Let $L$ be a Lie algebra‎, ‎$mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$‎. ‎We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields‎. ‎Also‎, ‎we classi...