SIMILARITY REDUCTIONS AND INTEGRABILITY FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL WITH SYMBOLIC COMPUTATION

Bo Tian, Wei Li and Yi-Tian Gao
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Bo Tian: School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
Wei Li: State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Yi-Tian Gao: Institute of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 02, 215-220

Abstract: The direct reduction method and computerized symbolic computation are extended to the Brusselator reaction–diffusion model, which describes a biochemical system and consists of two coupled nonlinear partial differential equations. New similarity reductions are obtained, which could be of biochemical interest. The resulting nonlinear ordinary differential equation in one dynamical variable cannot be transformed into any of the six standard forms which have solutions in terms of the Painlevé transcendents. Thus, the Brusselator model is not integrable according to the Painlevé conjecture.

Keywords: Symbolic computation; Brusselator reaction–diffusion model; similarity reductions; integrability (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0129183103004371

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