On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations
The authors present a direct and unifying scheme for the disclosure of bilinear Bäcklund transformations and linear Lax systems associated with the soliton equation. The scheme is based on a concept of scale invariance and on the use of a class of partitional polynomials: the binary Bell polynomials. In order to provide a complete picture of the method they start their discussions with the case of NLPDEs which can be derived from a quadratic Hirota equation, considering two simple examples: the KdV equation and the Sawada-Kotera equation.
scientific article; zbMATH DE number 1755370