ON THE EQUIVALENCE OF LINEARIZATION AND FORMAL SYMMETRIES AS INTEGRABILITY TESTS FOR EVOLUTION-EQUATIONS

Gurses' integrability test consists of the compatibility of the linear ized equation with an eigenvalue equation and leads to the recursion o perator. This test is applied to quasilinear fifth-order equations and the same classification as the 'formal symmetry' method of Mikhailov et al is obtained. The same classification for polynomial equations is obtained using Fokas' test, i.e. the existence of one higher-order sy mmetry. It is shown that the recursion operators of a specific form ca n be constructed using symmetries and conserved covariants and the rec ursion operators for polynomial equations are obtained with this metho d.