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We study analytically and numerically moving localized excitations of Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of large-amplitude strongly localized "discrete" kink-solitons (DK’s) which move with supersonic velocity which is proportional to the kink amplitude. For the FPU lattice, our numerical simulations also reveal two "discrete" subsonic group velocities of the moving large amplitude breathers which are both proportional to the breather amplitude. The main properties (relative displacement pattern, velocity, dispersion relation) of the observed super- and subsonic nonlinear excitations are well described analytically within theoretical approach based on the existence in FPU lattices of extended exact solutions with sinusoidal displacement pattern with "magic" wavenumber. |
