Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation...

Lie group theory states that knowledge of a m-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by m the number of equations. We apply this principle by finding some affine derivations that induces expanded Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we reduce...

This paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which has been presented by the author. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the longtime behavior of the original dynamical system. Those methods can be used in analyzing not only ordinary different...

Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are represented by onshell closed forms of various degrees. This extends the usual Noether’s correspondence between global symmetries and conservation laws to t...

A group invariant solution for a steady two-dimensional jet is derived by considering a linear combination of the Lie point symmetries of Prandtl’s boundary layer equations for the jet. Only two Lie point symmetries contribute to the solution and the ratio of the constants in the linear combination is determined from conservation of total momentum flux in the downstream direction. A conservatio...