  For travelling waves with nonzero boundary conditions, we justify the
logarithmic Korteweg-de Vries equation as the leading approximation of the
Fermi-Pasta-Ulam lattice with Hertzian nonlinear potential in the limit of
small anharmonicity. We prove control of the approximation error for the
travelling solutions satisfying differential advance-delay equations, as well
as control of the approximation error for time-dependent solutions to the
lattice equations on long but finite time intervals. We also show nonlinear
stability of the travelling waves on long but finite time intervals.
