a diffusion equation with exponential nonlinearity recant developments

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 therefore the general. we determine the classical lie point symmetriesincluding algebraic properties whereas similarity solutions are given as well as nonlineartransformations could derived. in addition, we discuss the nonclassical case which seems tobe not solvable. moreover we show how one can deduce approximate symmetries modelingthe nonlinear part and we deduce new generalized symmetries of lower symmetry. theanalysis allows one to deduce wider classes of solutions either of practical and theoreticalusage in different domains of science and engineering.