Eur. Phys. J. B (2018) 91: 242
https://doi.org/10.1140/epjb/e2018-90217-3

Regular Article

Modulational instability and peak solitary wave in a discrete nonlinear electrical transmission line described by the modified extended nonlinear Schrödinger equation

¹ Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR-2MSP), Faculté des Sciences, Université de Dschang, BP 69 Dschang, Cameroon
² Department of Physics, Higher Teacher Training College Bambili, University of Bamenda, PO Box 39, Bamenda, Cameroon

^a e-mail: fbpelap@yahoo.fr

Received: 29 March 2018
Accepted: 22 June 2018
Published online: 10 October 2018

Abstract

The present work describes the propagation of plane and peak solitary waves in a modified extended nonlinear Schrödinger (MENLS) equation that was earlier shown to govern the dynamics of modulated waves in a discrete nonlinear electrical transmission line (DNLETL). Firstly, the analytic expression for the modulational instability gain is found and the influence of wavenumber and wave amplitude on the gain is derived. It is predicted that they can be used to control the occurrence of modulation instability phenomenon in the network. Afterwards, using the MENLS equation, we show that this model of nonlinear electrical transmission line admits peak solitary wave for physically realistic parameters of the system. Direct numerical simulations are performed on the exact equations of the lattice and the obtained results are in very good agreement with the analytical predictions.