On application of Liouville type equations to constructing Bäcklund transformations

Abstract

It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the Bäcklund transformations. Several new examples of such transformations are found. In particular we obtained the Bäcklund transformations for a pair of three-component analogs of the dispersive water wave system, and auto-Bäcklund transformations for coupled three-component KdV-type systems.

11 pages, no figures

References in corpus (1)

• New integrable string-like fields in 1+1 dimensions

Cited by in corpus (2)

• Algebraic properties of Gardner's deformations for integrable systems
• On non-Abelian Toda $A_2^{(1)}$ model and related hierarchies