| Summary: | In this work, we provide a generalization of the β-Fermi–Pasta–Ulam–Tsingou (FPUT) chains which considers the absolute value of a power-law in a semi-infinite interval of the real line. It is well known that the β-FPUT chain shows the presence of nonlinear supratransmission, but not the α-FPUT model. The purpose of this work is to provide a generalization of the β-FPUT chain which considers potentials with arbitrary real power-laws, in such way that supratransmission is present independently of the value of the power. The systems considered in this work are all Hamiltonian, and we will use a Hamiltonian numerical discretization of the system to produce simulations. In our computational experiments, we will consider finite FPUT arrays which are perturbed sinusoidally on one end, and have a free boundary on the other. The system will be initially at rest, and the particles will be in resting position. For illustration purposes, we will consider various particular cases in order to exhibit the existence of supratransmission in those models, both in the undamped and the damped scenarios. Bifurcation diagrams will be obtained for various values of the power-law orders, and we will elucidate the behavior of the supratransmission threshold as a function of the driving amplitude and the power-law order.
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