paper

Supratransmission in Lattices with Purely Nonlinear Coupling

arXiv:2606.19237 · doi:10.1103/x5m6-wqkm

Abstract

Supratransmission is examined in nonlinear lattices with purely nonlinear coupling, extending the phenomenon to systems that lack a linear pass band. In contrast to standard lattices with mixed linear-nonlinear interactions, the present model has no linear spectrum, so energy propagation arises entirely from nonlinear effects. Asymptotic analysis yields a discrete -Schrödinger (DpS) equation that {provides an accurate description in the weak- and intermediate-coupling regimes and offers qualitative insight in the strong-coupling regime}. Perturbation provides analytical approximations for the critical driving amplitude, explicitly showing its dependence on the driving frequency, coupling strength, and the nonlinearity exponent . The analysis identifies a non-trivial dependence of the critical amplitude on , with distinct trends in different coupling regimes. Numerical continuation and direct simulations {validate the theory in regimes where the asymptotic reduction is applicable and show good agreement across a wide range of parameters}. The results establish supratransmission in fully nonlinear lattices and clarify the associated energy-transport mechanisms, with relevance to mechanical lattices, tunable metamaterials, and nonlinear optical arrays.

20 pages, 8 figures

References in corpus (10)