A base-equation method is implemented to realize the hereditary algebra of the Korteweg-de Vries (KdV) hierarchy and the N-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. Significantly enough, base functions themselves are found to provide a basis to regard the KdV-like equations as higher order degenerate bi-Lagrangian systems.
Volume 97, 2023
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