Narrow Results

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, $exp(-\chi (\xi ))$-expansion function method and $\frac{{\mathrm{\Theta }}^{\prime }(\xi )}{{\mathrm{\Theta }}^2(\xi )}$ expansion method. Numerical simulation is used to follow the dynamics of the system and to investigate its physical properties.

In this paper, the modified Jacobi elliptic function method is applied for Salerno equation which describes the nonlinear discrete electrical lattice in the forbidden bandgaps. Dark and bright solitons are obtained. Also, periodic solutions and periodic Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, three-dimensional and two-dimensional graphs are presented.