https://doi.org/10.1140/epjp/i2013-13063-7
Regular Article
On the propagation of nonlinear signals in nonlinear transmission lines
1
National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, 100190, Beijing, P.R. China
2
Département d’informatique et d’ingénierie, Université du Québec en Outaouais, 101 St-Jean-Bosco, J8Y 3G5, Gatineau, Canada
3
Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward Ave., ON K1N 6N5, Ottawa, Canada
* e-mail: ekengne6@yahoo.fr
Received:
1
February
2013
Revised:
28
April
2013
Accepted:
15
May
2013
Published online:
20
June
2013
A quintic nonlinear Schrödinger (NLS) equation, with derivative cubic terms, that governs the propagation of nonlinear signals in a nonlinear transmission line (NLTL) is considered. By combining a special phase-imprint transformation with a modified lens transformation, we reduce the equation under consideration to a standard cubic NLS equation with a time-varying gain/loss term and obtain the integrability condition. Under this condition, we first apply a superposition procedure to derive new nonlinear wave signals that propagate with periodic amplitude in the NLTL. Secondly, in the absence of any gain/loss term in the cubic NLS equation, we apply the Darboux transformation to the derived new bright soliton-like signal of the NLTL. For a special form of the gain/loss term of the cubic NLS equation, we combine the homogeneous balance principle and an F-expansion technique to show the propagation of both bright and dark soliton-like signals in the NLTL under consideration, and show how to manage the soliton motion in the line.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2013
