6533b821fe1ef96bd127af4a

RESEARCH PRODUCT

Energy localization in a nonlinear discrete system

Jean-marie BilbaultPatrick Marquié

subject

Discrete systemNonlinear systemDiscrete equationModulational instabilityAmplitudeLattice (order)Mathematical analysisContinuous wavePeriodic boundary conditions[ NLIN.NLIN-PS ] Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS]Mathematics

description

International audience; We show that, in the weak amplitude and slow time limits, the discrete equations describing the dynamics of a one-dimensional lattice can be reduced to a modified Ablowitz-Ladik equation. The stability of a continuous wave solution is then investigated without and with periodic boundary conditions; Energy localization via modulational instability is predicted. Our numerical simulations, performed on a cyclic system of six oscillators, agree with our theoretical predictions.

https://hal.archives-ouvertes.fr/hal-00650080