Transverse Stability in the Discrete Inductance-Capacitance Electrical Network

Eric Tala-Tebue, Aurelien Kenfack-Jiotsa

Laboratory of Mechanics, Department of Physics, Faculty of Sciences, University of Yaounde I, Yaounde, Cameroon.
Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teachers’ Training College, University of Yaounde I, Yaounde, Cameroon.

DOI: 10.4236/jmp.2013.46101                

Abstract

This work investigates the dynamics of modulated waves in a coupled nonlinear LC transmission line. By means of a method based on the semi-discrete limit and in suitably scaled coordinates, we derive the two-dimensional NLS equation governing the propagation of slowly modulated waves in the network. The exact transverse solution is found and the analytical criteria of stability of this solution are derived. The condition for which the network can exhibit modulational instability is also determined. The exactness of this analytical analysis is confirmed by numerical simulations performed on the exact equation of the network.

Keywords

Two-Dimensional Nonlinear Schrödinger Equation; Exact Transverse Solution; Stability; Modulational Instability

Conflicts of Interest

The authors declare no conflicts of interest.

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