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

V.P. Gerdt

Mathematics and Computers in Simulation (MATCOM), 1996, vol. 42, issue 4, 399-408

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:42:y:1996:i:4:p:399-408

DOI: 10.1016/S0378-4754(96)00015-8

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