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Homogeneity of integrability conditions for multi-parametric families of polynomial-non-linear evolution equations

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  • Gerdt, V.P.

Abstract

In this paper we consider the integrability conditions for multi-parametric families of polynomial-non-linear evolution equations with arbitrary parameters as coefficients of differential monomials. These conditions are the necessary ones for the existence of higher-order evolutionary symmetries and conservation laws. Their verification forms the basis for one of the most efficient integrability criteria which is valid both for one-component and multi-component quasi-linear evolution equations in one-temporal and one-spatial dimensions. We show that the integrability conditions, being a system of polynomial equations in arbitrary parameters, in the case of evolution equations with uniform rank have non-trivial homogeneity properties. It allows one to use efficiently the Gröbner bases method combined with the special reduction procedure for homogeneous polynomial systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:42:y:1996:i:4:p:399-408
    DOI: 10.1016/S0378-4754(96)00015-8
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    1. 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.
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