Abstract
In this article, we will introduce the mathematical model of the diffusion process in a swelling medium that has already been modeled. The main purpose of this paper is introducing a new class of group transformations for solving the nonlinear emulsion equation. Thus, we introduce this method as the discrete group methods based on solvable class orbits. One of the crucial advantages of this method is that a transformation is sought, which reduces the equation being investigated to some standard form for which the methods of integration are known. In developing this approach, one may construct all canonical forms of solvable equations.
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