Nonclassical symmetry reductions for an inhomogeneous nonlinear diffusion equation

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].…”

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

“…In [26], connection between classes of nonclassical and potential nonclassical symmetries of (5) and some new generators has been found. In [27,28], with n =− 1, we have derived nonclassical symmetries for (1), and for the associated system given by…”

Conditional Lie–Bäcklund symmetries and differential constraints for inhomogeneous nonlinear diffusion equations due to linear determining equations

“…INDE (1.8) has been used to model successfully physical situations involving diffusion processes in a wide range of fields [35,36]. A considerable number of literatures have been devoted to study symmetry related works about this equation and its variant generalized forms, including classical and nonclassical symmetry [37]- [40], potential and nonclassical potential symmetry [41]- [44]. CLBSs of Eq.…”