Abstract
In this paper, the potential symmetry method is developed to study systems of nonlinear diffusion equations. Potential variables of the systems are introduced through conservation laws; such conservation laws yield equivalent systems-auxiliary systems of PDEs with the given dependent and potential variables as new dependent variables. Lie point symmetries of the auxiliary systems which cannot be projected to the vector fields of the given dependent and independent variables yield potential symmetries of the systems. Classification for systems of nonlinear diffusion equations with two and three components is performed. Symmetry reductions associated with the potential symmetries are presented.
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