Backlund Transformations: a Link Between Diffusion Models and Hydrodynamic Equations

摘要

This work presents a new analytical method to transform exact solutions of linear diffusion equations into exact ones for nonlinear advection-diffusion models. The proposed formulation, based on Backlund transformations, is employed to obtain velocity fields for the unsteady two-dimensional Helmholtz equation, starting from analytical solutions of a heat conduction type model.