On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems

Abstract

We present an algorithmic method for obtaining an hereditary symmetry (the generalized squared-eigenfunction operator) from a given isospectral eigenvalue problem. This method is applied to the n×n eigenvalue problem considered by Ablowitz and Haberman and to the eigenvalue problem considered by Alonso. The relevant Hamiltonian formulations are also determined. Finally, an alternative method is presented in the case two evolution equations are related by a Miura type transformation and their Hamiltonian formulations are known.