Some aspects of Q-conditional symmetry and of its connections with reduction and compatibility are discussed. There are a number of examples in the history of science when a scientific theory quickly developed, gave good results and applications, and had no sufficiently good theoretical fundament. Let us remember mathematical analysis in the XVIII-th century. It is true in some respect for the ...

The nonclassical symmetries of boundary layer equations for two-dimensional and radial flows are considered. A number of exact solutions for problems under consideration were found in the literature, and here we find new similarity solution by implementing the SADE package for finding nonclassical symmetries.

• Symmetry analysis of differential equations: classical and nonclassical symmetries, potential symmetries, group–invariant solutions, variational symmetries and conservation laws • Applications of symmetry analysis theory to mathematical models arising in mathematical physics, mathematical biology, image processing, engineering, financial mathematics and other research fields • Geometric appro...

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations utt = ( κu+ γu ) xx + uuxxxx + μuxxtt + αuxuxxx + βu 2 xx , (1) where α, β, γ, κ and μ are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further ...

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as...

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...

A new technique for deriving the determining equations of nonclassical symmetries associated with a partial differential equation system is introduced. The problem is reduced to computing the determining equations of the classical symmetries associated with a related equation with coefficients which depend on the nonclassical symmetry operator. As a consequence, all the symbolic manipulation pr...

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...