TITLE:
Transverse Stability in the Discrete Inductance-Capacitance Electrical Network
AUTHORS:
Eric Tala-Tebue, Aurelien Kenfack-Jiotsa
KEYWORDS:
Two-Dimensional Nonlinear Schrödinger Equation; Exact Transverse Solution; Stability; Modulational Instability
JOURNAL NAME:
Journal of Modern Physics,
Vol.4 No.6,
June
13,
2013
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.