Baecklund transformations: a tool to study Abelian and non-Abelian nonlinear evolution equations
The KdV eigenfunction equation is considered: some explicit solutions are constructed. These, to the best of the authors’ knowledge, new solutions represent an example of the powerfulness of the method de- vised. Specifically, Ba ̈cklund transformation are applied to reveal alge- braic properties enjoyed by nonlinear evolution equations they connect.