Dynamics of modulated wave trains in a discrete nonlinear-dispersive dissipative Bi-inductance transmission line

In this paper nonlinear-dispersive dissipative RLC transmission line is considered and envelope modulation is reduced to the modified cubic-quintic complex Ginzburg-Landau equation (CGLE) with derivatives in cubic terms. This CGLE obtained contains two free (from the line parameters) parameters, the nonlinear cubic gain and the linear gain. Modulational instability for the modified cubic-quintic CGLE is analyzed and leads to the generalized Lange and Newell criterion. We reformulate the derived CGLE as a third-order ordinary system in standard form with the first derivatives on the left-hand side in order to study the coherent structures.