Solutions through nonclassical potential symmetries for a generalized inhomogeneous nonlinear diffusion equation

Abstract

SUMMARYIn this paper, we consider a class of generalized diffusion equations which are of great interest in mathematical physics. For some of these equations that model fast diffusion, nonclassical and nonclassical potential symmetries are derived. These symmetries allow us to increase the number of solutions. These solutions are unobtainable neither from classical nor from classical potential symmetries.

Nonclassical symmetry reductions for an inhomogeneous nonlinear diffusion equation

“…We can distinguish the following cases: If n v 5 0 by solving (24) and substituting into (25)-(27) leads to generators for which (22) is satisfied, consequently they are nonclassical potential generators and have been considered in [13].…”

Nonclassical Potential System Approach for a Nonlinear Diffusion Equation

“…In [21] it also appear in explicit form To obtain nonclassical symmetries of (1.19), we require that the PDE (1.19) and the invariance surface condition…”

Conditional Lie–Bäcklund symmetries and solutions of inhomogeneous nonlinear diffusion equations

“…A number of methods relating to symmetry groups have been successfully used to find the exact solutions and symmetry reductions of various special forms and generalized forms of (1.1), including the classical and nonclassical method [7][8][9][10][11][12][13][14][15][16], and the potential and nonclassical potential method [16][17][18][19][20][21][22]. It has been found that the symmetry group methods are effective to classify the equations or to identify the functions in the equations with respect to given symmetries [23,24].…”