Modulational instability and discrete localized modes in a nonlinear electrical transmission line with imaginary resistance

This study underscores the impact of imaginary resistance on modulational instability (MI) and the evolution of discrete localized modes in a nonlinear electrical lattice. The discrete nonlinear Schro¨dinger amplitude equation is derived from the circuit equations, by exploiting the rotating wave approximation perturbation method. Once a certain critical plane wave amplitude given by |ψ0,cr|2=2D1cos(k)sin2Q2/D2 is exceeded, modulationally unstable regions are obtained for both unstaggered and staggered waves, with maximum MI gain diminishing as the imaginary resistance increases. Analytical solutions are also derived as intrinsic localized discrete modes in the nonlinear electrical transmission line, with variation of imaginary resistance playing the important role of a control circuit parameter.