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Computer Algebra, Symmetry Analysis And Integrability Of Nonlinear Evolution Equations

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  • VLADIMIR P. GERDT

    (Laboratory of Computing Techniques and Automation, Joint Institute for Nuclear Research, Head Post Office P.O. Box 79, 141980 Dubna, Russia)

Abstract

A computer algebra-aided symmetry approach to investigating integrability of polynomial-nonlinear evolution equations in one-temporal and one-spatial dimensions is presented. The approach is based on verifying the existence of higher conservation laws and symmetries. If the equations contain arbitrary numerical parameters, the problem of selection of all the integrable cases is reduced to the solving polynomial equations in those parameters. The Gröbner basis technique is used in order to simplify and to solve such polynomial systems which typically have infinitely many solutions.

Suggested Citation

  • Vladimir P. Gerdt, 1993. "Computer Algebra, Symmetry Analysis And Integrability Of Nonlinear Evolution Equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 279-286.
    • Handle: RePEc:wsi:ijmpcx:v:04:y:1993:i:02:n:s012918319300029x
    DOI: 10.1142/S012918319300029X
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    Cited by:

    1. Gerdt, V.P., 1996. "Homogeneity of integrability conditions for multi-parametric families of polynomial-non-linear evolution equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 42(4), pages 399-408.

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