Spectral decompositions in nonlinear coupled diffusion

The solutions of a coupled, linear and nonlinear diffusion equationin a semi-infinite medium are derived using series methods.In addition, perturbation techniques allied to the spectraldecomposition of matrices are used to simplify the analysisand to find semianalytic solutions. The discussion is motivatedby the transmission of heat, moisture, and solute through thestrongly nonlinear medium of soil. Under boundary conditionsrepresenting the daily or seasonal fluctuations, it is shownusing spectral decomposition, despite the nonlinearities, howthe period of oscillation is preserved on passage through themedium. It is also shown how n³ partial differential equationsmay be solved for each of the n coupled variables to determineclosed forms for the first- and second-order perturbation effects.Examples of the solutions are given for the case of the coupledtransport of heat and moisture in soil.