arXiv subjects

Tomasz Czyżycki

Publications and source records attributed to Tomasz Czyżycki.

2 recordsLinked to original sources

arXiv2017

Non-point symmetry reduction method of partial differential equations

We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of non-point classical and conditional symmetry. Then we find solution to nonlinear heat equation which can not be obtained in the framework of the classical Lie approach. By using operators of Lie--Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too. We show that the method can be applied to nonevolutionary partial differential equations.

math.AP↗

arXiv2014

Generalized discrete orbit function transforms of affine Weyl groups

The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the shifted weight and the shifted dual weight lattices, which serve as a sampling grid and a set of labels of the orbit functions, respectively, are introduced. The complete sets of discretely orthogonal orbit functions over the sampling grids are found and the corresponding discrete Fourier transforms are formulated. The eight standard one-dimensional discrete cosine and sine transforms form special cases of the presented transforms.

math-ph↗