For the nite Schur (dmKdV) ows, a nonlocal Poisson structure is introduced and shown to be linked via BB acklund-Darboux transformations to linear and quadratic Poisson structures for the Toda lattice. Two diierent Lax representation for the Schur ows are used, one to construct BB acklund-Darboux transformations, the other to solve the Cauchy problem via the trigonometric moment problem.

It is shown that for each k > 1, if f is a Baire one function and f is the product of k bounded Darboux (quasi–continuous) functions, then f is the product of k bounded Darboux (quasi–continuous) Baire one functions as well.

A version of the iterated Bäcklund-Darboux transformation, where Darboux matrix takes a form of the tranfer matrix function from the system theory, is introduced for the discrete canonical system and nonAbelian Toda lattice. Solutions are constructed and several spectral results are obtained.

Application of the double Darboux method to the quantum Taub continuum Abstract The strictly isospectral double Darboux method is applied to the quantum Taub model in order to generate a one-parameter family of strictly isospectral potentials for this case. The family we build is based on a scattering Wheeler-DeWitt solution first discussed by Ryan and collaborators that we slightly modified ac...