COMPUTATIONAL STUDY OF THE TRANSMISSION OF ENERGY IN A TWO-DIMENSIONAL LATTICE WITH NEAREST-NEIGHBOR INTERACTIONS

In this work, we establish computationally the existence of the process of nonlinear supratransmission in the simplest generalization of the classical -Fermi{Pasta{Ulam chain to two-space dimensions, subject to harmonic boundary data in one end of the Dirichlet form. Our simulations employ a nite-dierence scheme with multiple properties of consistency in the domains of the solutions, the local energy density and the total energy of the system. Moreover, our results establish the presence of the phenomenon of nonlinear infratransmission or lower-transmission, thus proving the existence of a bistable region where a conducting and an insulating regimes coexist.