Eur. Phys. J. B 27, 329-334 (2002)
https://doi.org/10.1140/epjb/e2002-00162-5

Anharmonic excitations in the FPU and FK models

¹ Laboratoire de Physique Théorique de la Matière Condensée, Université Paris 7, case 7020, 2 Place Jussieu, 75251 Paris Cedex 05, France
² Department of Physics, East China Normal University, Shanghai 200062, PR China

Corresponding author: ^a szeftel@ccr.jussieu.fr

Received: 7 November 2001
Revised: 5 February 2002
Published online: 6 June 2002

Abstract

The properties of vibrational localized (breathers) and traveling (anharmonic phonons) waves are discussed in an infinite, one-dimensional, monoatomic crystal for the Fermi-Pasta-Ulam and Frenkel-Kontorova models. The shooting and finite difference schemes have been implemented to reckon the displacement fields of breathers and anharmonic phonons, respectively. These tools provide localized and traveling waves proving to be indefinitely stable in simulations carried out by solving the equations of motion. The emphasis is laid on the role of the cubic and quartic terms of the anharmonic potential which turn out to oppose and to shore up the restoring force, respectively. The case of vibrational modes arising in an anharmonic crystal subject to a soft phonon induced instability is also addressed.