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Similarity Reductions And Integrability For The Brusselator Reaction–Diffusion Model With Symbolic Computation

Author

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  • BO TIAN

    (School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
    State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, 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;
    State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100083, China)

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.

Suggested Citation

  • Bo Tian & Wei Li & Yi-Tian Gao, 2003. "Similarity Reductions And Integrability For The Brusselator Reaction–Diffusion Model With Symbolic Computation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 215-220.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:02:n:s0129183103004371
    DOI: 10.1142/S0129183103004371
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