  We analyze the relationship between the lowest energy configurations of an
infinite harmonic chain of particles in a periodic potential and the evolution
of characteristics in a periodically-forced inviscid Burgers equation. The
shock discontinuities in the the Burgers evolution arise from thermodynamical
considerations and play an important role as they separate out flows related to
lowest energy configurations from those associated with higher energies. We
study in detail the exactly solvable case of an external potential consisting
of parabolic segments, and calculate analytically the lowest energy
configurations, as well as excited states containing discommensurations.
