Abstract
We perform a complete group classification of a coupled system of diffusion equations with applications in soil science. The canonical forms of the lowdimensional Lie algebras and the Lie algebras of higher dimension provide a means to specify the diffusion coefficients completely.
Highlights
A group classification for a general second-order system of diffusion equations based on Lie algebras of low dimension was performed in [1]
The classification procedure involves the utilization of the structure of the low-dimensional Lie algebras and the Lie algebras of higher dimension to find the symmetry operators admitted by the underlying equation or system
When we look at the above functional forms of the diffusion coefficients, the cases A32,2 and A42,2 can be regarded as one case for a choice of equivalence transformations of the form t = t, x = x, u = v, v = u
Summary
A group classification for a general second-order system of diffusion equations based on Lie algebras of low dimension was performed in [1]. The equivalence group is used to obtain the canonical forms of the symmetry operators which satisfy the model under consideration Even though this procedure was suggested in [2, 3] for partial differential equations (PDEs), a much earlier work on ordinary differential equations (ODEs) using these ideas was done in [4]. Wiltshire et al [11, 13] investigated the Lie symmetries of a simplified model of the coupled diffusion system (1) written in the form yt = [Λ(y)yx]x , y = {yi} The generation of the determining equations and the manipulation of them are with the aid of the YaLie software package [14]
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