Nonlinear supratransmission revisited
Résumé
Nonlinear Supratransmission (NST) was discovered by J. Léon and F. Geniet [Phys. Rev. Lett. 89, 134102 (2002)] in a chain of coupled pendula forced harmonically at one end with a frequency lying within the chain forbidden band gap. When the forcing amplitude is low enough, an evanescent wave is formed that becomes unstable at a critical value above which a sudden energy transfer occurs through the emission of gap solitons: this is NST. This phenomenon has since been observed in many different contexts and in particular in some continuous non integrable multicomponent Nonlinear Schrödinger like models used in Optics. For such models, the NST threshold is a surface whose dimension is equal to the number of components (fields) involved. I shall present an asymptotic method that permits its determination and also talk about an ultra-discrete (monomer) approach that yields both simple and reliable analytical expressions for NST manifolds.