Europhys. Lett.
Volume 66, Number 1, April 2004
Page(s) 21 - 27
Section General
Published online 01 March 2004
Europhys. Lett., 66 (1) , pp. 21-27 (2004)
DOI: 10.1209/epl/i2003-10156-5

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

Yu. A. Kosevich1, R. Khomeriki2 and S. Ruffo3, 4

1  Instituto de Investigación en Comunicación Optica Universidad Autonóma de San Luis Potosí, Alvaro Obregon 64 78000 San Luis Potosí, SLP, Mexico
2  Department of Physics, Tbilisi State University - 3 Chavchavadze avenue Tbilisi 380028, Republic of Georgia
3  Dipartimento di Energetica "Sergio Stecco" and CSDC Università di Firenze Via S. Marta, 3, I-50139 Firenze, Italy
4  INFM and INFN - Firenze, Italy

(Received 24 March 2003; accepted in final form 3 February 2004)

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 $k=2\pi/3$. 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.

05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
63.20.Pw - Localized modes.

© EDP Sciences 2004