Related papers: Symmetry classification of third-order nonlinear e…

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.

Non-degenerate bilinear forms over fields of characteristic 2, in particular, non-symmetric ones, are classified with respect to various equivalences, and the Lie algebras preserving them are described. Although it is known that there are…

A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…

We present classification of Q-conditional symmetries for the two-dimensional nonlinear wave equations and the reductions corresponding to these nonlinear symmetries. Classification of inequivalent reductions is discussed.

A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…

We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.

Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…

The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…

A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimensional solvable Lie algebras (over fields of any…

In this note we present three representations of a 248-dimensional Lie algebra, namely the algebra of Lie point symmetries admitted by a system of five trivial ordinary differential equations each of order forty-four, that admitted by a…

We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution…

We complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to…

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…

A symmetry classification of possible interactions in a diatomic molecular chain is provided. For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant and taking solutions into solutions, is at most…

We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…

The solution of a class of third order ordinary differential equations possessing two parameter Lie symmetry group is obtained by group theoretic means. It is shown that reduction to quadratures is possible according to two scenarios: 1) if…

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a…