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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

UFRGS, Porto Alegre, RS, Brazil.
UniRitter, Porto Alegre, RS, Brazil.

Computer Modeling in Engineering & Sciences 2014, 103(4), 215-227. https://doi.org/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.

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Zabadal, J., Bodmann, B., Ribeiro, V. G., Silveira, A., Silveira, S. (2014). Bäcklund Transformations: a Link Between Diffusion Models and Hydrodynamic Equations. CMES-Computer Modeling in Engineering & Sciences, 103(4), 215–227.



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