Eur. Phys. J. Plus (2021) 136: 710
https://doi.org/10.1140/epjp/s13360-021-01683-7

Regular Article

Optical solitons to the nonlinear Schrödinger equation in metamaterials and modulation instability

¹ Department of Basic Science, Faculty of Mines and Petroleum Industries, University of Maroua, P.O Box 08, kaélé, Cameroon
² Laboratory of Mechanics, Materials and Structures, Department of physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
³ Department of Physics, Faculty of Science, University of Maroua, P.O Box 814, Maroua, Cameroon
⁴ Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran
⁵ Biruni University, Deprtment of Computer Engineering, Istanbul, Turkey
⁶ Firat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey
⁷ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
⁸ Department of Physics, Faculty of Science, University of Ngaoundere, P.O Box 454, Ngaoundere, Cameroon
⁹ National Advanced School of Engineering, University of Yaounde I, Yaounde, Cameroon

^a abbagaris@yahoo.fr
^b ahouw220@yahoo.fr
^e minc@firat.edu.tr

Received: 10 April 2021
Accepted: 18 June 2021
Published online: 2 July 2021

Abstract

Throughout this paper, we investigate the propagation of solitary waves in metamaterials. Indeed, we focus our attention on a nonlinear evolution equation, namely the nonlinear Schrödinger equation (NLSE) that models the dynamic of waves in such materials. Investigating solitons structures of such an equation, we make use for the purpose, of a mathematical tool which is a new generalized extended direct algebraic method (NGEDAM). As a results, rich solution structures are constructed analytically to which new solutions are provided to complete the ones already obtained elsewhere. In addition, the modulation instability (MI) analysis has been studied by employing the linearizing technic. We highlight the effects of the self-steepening (SS) associated to metamaterials parameters on MI bands. The obtained results have set up the W-shaped profile of the optical soliton solutions, which will certainly improve the communication over the optical fibers in diverse modes.