It is well known that symmetry-based methods are very powerful tools for investigating
nonlinear partial differential equations (PDEs), notably for their reduction to those of lower …

A complete description of Q-conditional symmetries for a class of reaction–diffusion–
convection equations with exponential diffusivities is derived. It is shown that all the known …

A complete description of Q-conditional symmetries for two classes of reaction–diffusion–
convection equations with power diffusivities is derived. It is shown that all the known results …

Using enhanced classification techniques, we carry out the extended symmetry analysis of
the class of generalized Burgers equations of the form u t+ uu x+ f (t, x) u xx= 0. This …

The determining equations for the nonclassical reductions of a general nth order
evolutionary partial differential equations is considered. It is shown that requiring …

The notion of singular reduction modules, ie, of singular modules of nonclassical
(conditional) symmetry, of differential equations is introduced. It is shown that the derivation …

The nonclassical symmetries of a class of Burgers' systems are considered. This study was
initialized by Cherniha and Serov with a restriction on the form of the nonclassical symmetry …

Reduction operators of generalized Burgers equations are studied. A connection between
these equations and potential fast diffusion equations with power nonlinearity of degree− 1 …

It is known that Q-conditional symmetries of the classical Burgers' equation express in terms
of three functions satisfying a coupled system of Burgers-like equations. The search of …

The solution of the problem on reduction operators and nonclassical reductions of the
Burgers equation is systematically treated and completed. A new proof of the theorem on the …