Exact conserved quantities on the cylinder II: off-critical case

With the aim of exploring a massive family of models, the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in terms of the corresponding solutions of the nonlinear integral equation. The family of models turns out to correspond to the Phi((1,3)) perturbation of Conformal Field Theories. The analytic and asymptotic behaviours of the transfer matrix are studied and given.