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.

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• Bifurcations
• Energy transport
• Lattice dynamics
• Granular chains
• Nonlinear waves