Supratransmission in lattices with purely nonlinear coupling

Supratransmission is examined in nonlinear lattices with purely nonlinear coupling, extending the phenomenon to systems that lack a linear passband. 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 p-Schrödinger equation that provides an accurate description in the weak- and intermediate-coupling regimes and offers qualitative insight into 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 p. The analysis identifies a nontrivial dependence of the critical amplitude on p, 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.