The Revised Modulational Instability Criterion: I – The Mono-Inductance Transmission Line

Wave modulations in the mono-inductance transmission line are studied by the use of a perturbation method. Far from the marginal state, that is for wavenumbers k larger than a critical wavenumber k c the evolution of a wave packet is described by the nonlinear Schrödinger (NLS) equation. Near this critical state of instability, it has been shown the NLS equation is not appropriate. We demonstrated that, in such regime, wave propagations are governed by a modified form of the NLS equation that involves higher-order nonlinearities. The associated revised modulational instability criterion is obtained and corresponding exact solutions are presented.