Characteristic integrals and general solution of the Ferapontov-Shabat-Yamilov lattice

For the finite (non-periodic) systems obtained from a lattice introduced by Ferapontov and independently by Shabat and Yamilov, we present a quadrature-free general solution and a recurrent formula for the characteristic integrals. The derivation of these formulae relies on the underlying determinantal equations. We illustrate the results using a two-component system.