Non-isospectral extension of the Volterra lattice hierarchy, and Hankel determinants

For the first two equations of the Volterra lattice hierarchy and the first two equations of its non-autonomous (non-isospectral) extension, we present Riccati systems for functions c_j(t), j=0,1,..., such that an expression in terms of Hankel determinants built from them solves these equations on the right half of the lattice. This actually achieves a complete linearization of these equations of the extended Volterra lattice hierarchy.Comment: 31 pages, 3rd version: introduction extended, part of Section 2 moved there, Appendix D added, additional references, to appear in Nonlinearit

Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach

A proper bilinear form is proposed for the N=1 supersymmetric modified Korteweg-de Vries equation. The bilinear B\"{a}cklund transformation of this system is constructed. As applications, some solutions are presented for it.Comment: 8 pages, LaTeX using packages amsmath and amssymb, some corrections mad