Numerical study of the transmission of energy in discrete arrays of sine-Gordon equations in two space dimensions

In this paper, we provide a numerical approximation to the occurrence of the process of nonlinear supratransmission in semiunbounded, discrete, (2+1)-dimensional systems of sine-Gordon equations subject to harmonic Neumann boundary data irradiating with a frequency in the forbidden band gap. The model is a generalization of the one describing semi-infinite, discrete, (1+1)-dimensional, parallel arrays of Josephson junctions connected through superconducting wires, subject to the action of an ac current at the end. The computational results are obtained using a finite-difference scheme for sine-Gordon and nonlinear Klein-Gordon media, and the method is applied to systems of harmonic oscillators when Dirichlet data are imposed to the boundary. Our numerical results show that energy is transmitted into the medium in the form of discrete breathers.