Isogroup classification and group-invariant solutions of the nonlinear diffusion- convection equation T_t = (D_1(T)T_x)_x - D'_2(T)T_x

摘要

Herein the physically and mathematically significant nonlinear diffusion-convection equation which finds application in the theory of transport in porous media has been analysed using the isovector approach. A complete classification of isovector fields has been presented for 11 different forms of the functions of the dependent variable in the form of three tables. For a number of physically interesting cases, symmetry reductions have been performed which lead one to a number of new exact solutions. An interesting case of this study is Fokas-Yortsos equation (generalized Fokas-Yortsos equation) for which it has been shown that there are two exact solutions possible, out of which one is a travelling wave solution. Further, in a number of cases the nonlinear diffusion equation has been shown to be reducible to quadratures and standard second order nonlinear differential equations, specially for logarithmic and exponential function forms.