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Supratransmission in lattices with purely nonlinear coupling
Defri Ahmad1, Tae-Yeon Kim2,3, Andreas Schiffer4
1Khalifa University, Department of Mathematics, PO Box 127788 Abu Dhabi, United Arab Emirates.
Physical Review. E
|July 24, 2026
Summary
Supratransmission occurs in nonlinear lattices without linear passbands, driven solely by nonlinear effects. This study reveals critical amplitude dependencies and energy transport mechanisms in these unique systems.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Wave propagation
Background:
- Supratransmission typically requires a linear passband for energy propagation.
- Standard nonlinear lattices involve mixed linear-nonlinear interactions.
- This study investigates a novel system with purely nonlinear coupling.
Purpose of the Study:
- To examine supratransmission in nonlinear lattices lacking a linear passband.
- To understand energy propagation mechanisms driven entirely by nonlinear effects.
- To analyze the critical driving amplitude and its dependencies.
Main Methods:
- Asymptotic analysis to derive a discrete p-Schrödinger equation.
- Perturbation theory to approximate critical driving amplitude.
- Numerical continuation and direct simulations for validation.
Main Results:
- A discrete p-Schrödinger equation accurately describes weak and intermediate coupling.
- Analytical approximations reveal critical amplitude dependence on frequency, coupling, and nonlinearity exponent (p).
- Distinct trends in critical amplitude observed across different coupling regimes.
Conclusions:
- Supratransmission is established in fully nonlinear lattices.
- Energy transport mechanisms in these systems are clarified.
- Findings are relevant to mechanical lattices, metamaterials, and optical arrays.
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