Modulation instability and modulated wave patterns in a nonlinear electrical transmission line with the next-nearest-neighbor coupling

Abstract

In this paper, we investigate modulation instability and solitary waves in a one-dimensional nonlinear electrical transmission line with second-neighbor interactions. Through the quasi-discrete multiple scale method, we derive coupled nonlinear Schrödinger equations. To investigate the modulation instability in the structure, we use the linear stability analysis, and an expression for the modulation instability spectrum is derived. From the analytical investigation, we show that the second neighbor coupling affects both the modulation instability growth rate and modulation instability bands. Furthermore, we show via single and coupled mode excitation that bright and dark solitary waves can propagate at the lower and upper cutoff frequencies. To evaluate the robustness of the analytical investigation, we use a direct numerical simulation of the continuous wave. We conclude that the second-neighbor couplings generate rogue waves in the structure during the long-time evolution of the plane wave. We also demonstrate that with a variation of the excitation wave number, the nonlinear electrical transmission line can support new objects as wave molecules for high values of the wave number. This feature is not yet observed in nonlinear electrical transmission lines and will be useful in many fields of physics.