The sharp-pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of high-energy strongly localized "discrete" kink-solitons (DK), which move with supersonic velocities that are proportional to kink amplitudes. For small amplitudes, the DKs of the FPU lattice reduce to the well-known "continuous" kink-soliton solutions of the modified Korteweg-de Vries equation. For high amplitudes, we obtain a consistent description of these DKs in terms of approximate solutions of the lattice equations that are obtained by restricting to a bounded support in space exact solutions with sinusoidal pattern characterized by the "magic" wave number k = 2π/3. Relative displacement patterns, velocity vs. amplitude, dispersion relation and exponential tails found in numerical simulations are shown to agree very well with analytical predictions, for both FPU and LJ lattices.
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Kosevich et al. (2004) studied this question.
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