We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial diierential equations. Using the introduced deenition of reduction of diierential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential equat...

We give a comprehensive analysis of interrelations between the basic concepts of the modern theory of symmetry (classical and non-classical) reductions of partial differential equations. Using the introduced definition of reduction of differential equations we establish equivalence of the non-classical (conditional symmetry) and direct (Ansatz) approaches to reduction of partial differential eq...

Lie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numerical computations involve many different concepts. Therefore they give rise to numerical schemes that vary in the accuracy, in the computational cost and in the implementation. In this paper a comparison is made b...

Abstract The classical symmetry method is often employed to find precise solutions differential equations. This has yielded several new reductions and exact for numerous theoretically physically relevant partial These results, as well the symmetries of a variety specific cases Fokker–Planck equation, were presented in this study using Lie approach. New equations are provided each six cases.