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Supersonic discrete kink-solitons and sinusoidal patterns with “magic” wave number in anharmonic lattices

2003/03/31 by Yuriy A. Kosevich, Yu. A. Kosevich, Рамаз Хомерики +2
Physics and Astronomy · #Advanced Fiber Laser Technologies #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #cond-mat.stat-mech

paper · pdf · doi:10.1209/epl/i2003-10156-5

published as Europhys. Lett., v.66, 21 (2004). · Europhysics Letters (in print)

arxiv created 2004/01/25 · openalex publication_date 2004/04/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

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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