On mathematical analysis of a discrete electrical lattice with nonlinear dispersion

Abstract

In this paper, we consider the discrete electrical lattice with nonlinear dispersion described by Salerno equation, Fig. 1. Stability of equilibrium points, limit cycles and flip and Hopf bifurcations of the system are discussed. New exact solutions of a continuous approximation of the discrete system in the upper forbidden band gap are obtained by two methods, namely, exp(-χ(ζ))-expansion function method and ⊖′(ζ)/⊖2(ζ) expansion method. Numerical simulation is used to follow the dynamics of the system and to investigate its physical properties.