Propagating discrete breather due to plane wave in electrical transmission lattice with imaginary resistance

Abstract We examined the discrete nonlinear Schrödinger (DNLS) equation as a voltage on a discrete electrical line in the presence of an imaginary resistance. The continuous approximation of the steady state allows for acquiring a static breather, whose amplitude decreases when the imaginary resistance increases. The linear stability and the full integration lead to seeing that the breather is stable when the centre is in the middle of the lattice, but becomes unstable when it’s near the edge. The analytical amplitude of the static discrete breather matches very well with the numerical supratransmission threshold. A method for propagating discrete breathers is proposed. To achieve this, a static and unstable breather is shaken by periodic excitation of the chain with very small amplitude. By using a method, single and two traveling waves can be generated in the DNLS equation. This is not the case with the classical nonlinear band gap studies.