2016/11/30 by George Miloshevich, Jean Pierre Nguenang, Thierry Dauxois +2 · 1 citation
Physics and Astronomy · #nlin.PS #nlin.SI #physics.comp-ph
paper · pdf · doi:10.1088/1751-8121/aa5fcf
published as Journal of Physics A: Mathematical and Theoretical 50.12 (2017) · 10 pages, 4 figures
arxiv created 2017/08/06 · arxiv updated 2017/08/09
We investigate the existence and propagation of solitons in a long-range extension of the quartic Fermi-Pasta-Ulam (FPU) chain of anharmonic oscillators. The coupling in the linear term decays as a power-law with an exponent greater than 1 and less than 3. We obtain an analytic perturbative expression of traveling envelope solitons by introducing a Non Linear Schrodinger (NLS) equation for the slowly varying amplitude of short wavelength modes. Due to the non analytic properties of the dispersion relation, it is crucial to develop the theory using discrete difference operators. Those properties are also the ultimate reason why kink-solitons may exist but are unstable, at variance with the short-range FPU model. We successfully compare these approximate analytic results with numerical simulations.