Eur. Phys. J. Plus (2015) 130: 51
https://doi.org/10.1140/epjp/i2015-15051-3

Regular Article

Dynamics of localized electromagnetic waves for a cubic-quintic nonlinear Schrödinger equation

¹ Higher Teachers’ Training College of Maroua, The University of Maroua, PO Box 55, Maroua, Cameroon
² Centre d’Excellence en Technologie de l’Information et de la Communication, The University of Yaounde I, PO Box 812, Yaounde, Cameroon
³ Faculty of Sciences, The University of Maroua, PO Box 814, Maroua, Cameroon
⁴ Department of Physics, Faculty of Sciences, The University of Yaounde I, PO Box 812, Yaounde, Cameroon

^* e-mail: douvagai@yahoo.fr

Received: 27 August 2014
Revised: 24 December 2014
Accepted: 7 February 2015
Published online: 26 March 2015

Abstract

We consider the cubic-quintic nonlinear Schrödinger equation describing the propagation of femtosecond pulses in nonlinear optical fibers. Through analysis of different phase portraits, we predict the existence of solitary and periodic wave solutions of the previous equation. Numerical solutions confirm such existence. In addition, by using a special rational exponential ansatz, we find analytic solitary and periodic wave solutions. These interesting solutions may be useful to explain dynamical properties of optical traveling wave solutions.