  We construct one-dimensional nonlinear lattices having the special property
such that the Umklapp process vanishes and only the normal processes are
included in the potential functions. These lattices have long-range quartic
nonlinear and nearest neighbor harmonic interactions with/without harmonic
on-site potential. We study heat transport in two cases of the lattices with
and without harmonic on-site potential by non-equilibrium molecular dynamics
simulation. It is shown that the ballistic heat transport occurs in both cases,
i.e., the scaling law $\kappa\propto N$ holds between the thermal conductivity
$\kappa$ and the lattice size $N$. This result directly validates Peierls's
hypothesis that only the Umklapp processes can cause the thermal resistance
while the normal one do not.
