A New Derivation of the Bäcklund Transformation for the Volterra Lattice

Abstract

Using a lattice version of the Miura transformation between two nonlinear evolution systems called the Volterra lattice and the modified Volterra lattice, we have obtained a pair of Backlund transformations for the Volterra lattice onto itself. By this form of the transformations, we can show the relation between the inverse scattering problems and the discrete Miura transformation, then derive the conservation laws and the superposition formula. In a suitable continuum limit, they reduce to be a complete analogue of the Backlund transformations for the Korteweg-de Vries equations first obtained by Wahlquist and Estabrook.