Intrinsic localized modes as solitons with a compact support

It is shown that nonlinear localized modes in purely anharmonic lattices may be treated as compactons, i.e., solitons with finite wavelength [see Ph. Rosenau and J. M. Hyman, Phys. Rev. Lett. 70, 564 (1993)]. An explicit analytical solution for a compacton with an internal frequency is found for the chain of particles interacting via the quartic interatomic potential. It is demonstrated that in two particular cases, when the compacton is centered at a particle site or between neighboring particle sites, this solution gives exact expressions for two intrinsic localized modes found earlier in the framework of the rotating-wave approximation.