Relations among generalized Korteweg–deVries systems

Abstract

This report presents certain relations among the completely integrable Hamiltonian systems introduced by Gel’fand and Dikii. These relations generalize a formula of A. Lenard linking the higher‐order Korteweg–deVries equations, of which the Gel’fand–Dikii systems are a generalization. The general form of the relations, which connect the various isospectral deformations of linear differential operators, is described, and two examples are given explicitly.