  The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one
end fixed are computed exactly from the two-dimensional nonlinear Morse map.
These exact nonlinear structures are interpreted as domain walls (DW),
interpolating between bound and unbound segments of the chain. The free energy
of the DWs is calculated to leading order beyond the Gaussian approximation.
Thermodynamic instabilities (e.g. DNA unzipping and/or thermal denaturation)
can be understood in terms of DW formation.
