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Bäcklund Transformations: a Link Between Diffusion Models and Hydrodynamic Equations

J.R. Zabadal¹, B. Bodmann¹, V. G. Ribeiro², A. Silveira², S. Silveira²

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.4, pp. 215-227, 2014, DOI:10.3970/cmes.2014.103.215

Abstract 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 Bäcklund transformations, is employed to obtain velocity fields for the unsteady two-dimensional Helmholtz equation, starting from analytical solutions of a heat conduction type model. More >

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