Kortewega€“de Vries hierarchy using the method of base equations

摘要

A base-equation method is implemented to realize the hereditary algebra of the Kortewega€“de Vries (KdV) hierarchy and the e?‘?-soliton manifold is reconstructed. The novelty of our approach is that, it can in a rather natural way, predict other nonlinear evolution equations which admit local conservation laws. Signi???cantly enough, base functions themselves are found to provide a basis to regard the KdV-like equations as higher order degenerate bi-Lagrangian systems.