No abstract

The dynamics of modulated waves are studied in the one-dimensional discrete nonlinear electrical transmission line. The contribution of the linear dispersive capacitance is taken into account, and it is shown via the reductive perturbation method that the evolution of such waves in this system is governed by the higher-order nonlinear Schrödinger equation. Passing through the Stokes analysis, we establish a generalized criterion for the Benjamin-Feir instability in the network and determine the exact solutions of the obtained wave equation by using the Pathria-Morris approach.

Two-fold integrable hierarchy of nonholonomic deformation of the derivative nonlinear Schrödinger and the Lenells-Fokas equationDynamics of modulated waves is studied in a one-dimensional discrete nonlinear electrical transmission line. Contribution of a linear dispersive capacitance is appreciated and it is shown via a reductive perturbation method that evolution of such waves in this system is governed by a higher order nonlinear Schrödinger equation. Passing through the Stokes wave analysis, a generalized criterion for the Benjamin-Feir instability in the network is presented and exact solutions of the obtained wave equation are determined by the means of the Pathria and Morris approach.

We report on the experimental observation of the Fermi–Pasta–Ulam (FPU) recurrence in an experimental bi-modal nonlinear transmission line. The FPU recurrence is observed in the two transmission modes known as the low frequency mode and the high frequency mode. In each case, a spectrum analysis is performed in order to study the waves along the line.

Focused on the quintic complex Ginzburg-Landau equation used as the basic physical model, we have reviewed the well known Lange and Newell's criterion for modulational stability of Stokes waves.