Solitonic rogue waves induced by the modulation instability in a split-ring-resonator-based left-handed coplanar waveguide

Abstract

Modulation instability and nonlinear excitation modes in lower and upper frequency bands are investigated in the nonlinear left-handed coplanar waveguide, where nonlinear capacitance (voltage-dependent) is used. The multi-scale method is employed to derive a system of two coupled nonlinear Schödinger equations governing the evolution of the kink and bright solitons of these modes. A modulation instability is investigated to show the effects of the left-handed and right-handed influences on the modulation instability gain and the intensity of the plane wave. In the lower and upper frequency modes, the breathing structures have strong values for the left-handed component. At the end, the numerical simulation of the continuous wave is used to show the development of the modulated waves and localized objects. Another relevant localized structure has been obtained to display the second-order breathers and Akhmediev breathers of types A and B under the variation of the perturbed wave number. Both linear inductances and perturbed wave numbers are tools for controlling the amplitude of the localized structures, and modulation instability is sensitive to these parameters.