Excitation spectrum of the Toda lattice for finite temperatures

For the Toda lattice, the integral equations of Yang and Yang are derived for the classical limit and their analytical solutions are given. The introduction of renormalized energies eventually leads to a finite temperature excitation spectrum of classical solitons and semiclassical phonons. The excitation energies are tested by a comparison of the group velocities for vanishing momentum with the sound velocity which can be calculated directly from the thermodynamics.