A formula for obtaining new hereditary symmetries and new integrable equations

Abstract

In this paper we give a simple formula to obtain hereditary symmetries related to the isospectral eigenvalue problem of integrable equations. Using this formula, (i) we prove that eigenfunctions of hereditary strong symmetry are symmetries for the whole hierarchy, which improves the result of Fokas and Anderson [J. Math. Phys. 23, 1066 (1982)]; (ii) we find new integrable equations; and (iii) we give strong symmetries of these new integrable equations and various equations for eigenfunctions of the isospectral eigenvalue problems.