Spectral analysis of generalized Volterra equation

A generalized Volterra lattice with a nonzero boundary condition is considered by virtue of the inverse scattering transform. The two-sheeted Riemann surface associated with the boundary problem is transformed into the Riemann sphere by introducing a suitable variable transformation. The associated spectral properties of the lattice in single-valued variable was discussed. The constraint condition about the nonzero boundary condition and the scattering data is found.