We propose the unique one dimentional nonlinear lattice, which is called the umklapp free lattice (UFL), and the regime of cubic strong nonlinearity in its lattice is investigated. Ballistic thermal transport is observed in the UFL and its nature is invariant for the change of strength of nonlinearity. On the other hand, as the strength of cubic nonlinearity becomes stronger, the thermal conductivity in the UFL decreases. To explain its reduction, dispersion relations are derived numerically. It is revealed that bandwidth decrease as the strength of cubic nonlinearity increases. We also describe dispersion relation by using space-time Fourier transform. This results are good agreement with analytic dipersion relations in the regime of cubic strong nonlinearity. Moreover, the reduction of bandwidth corresponds to the decay of phonon group velocity and it causes the reduction of the thermal conductivity.
Ono et al. (Wed,) studied this question.