Eur. Phys. J. Plus (2020) 135: 380
https://doi.org/10.1140/epjp/s13360-020-00384-x

Regular Article

Exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr nonlinearity form using two strategic integrations.

¹ Department of Physics, Faculty of Science, the University of Maroua, P.O. Box 814, Maroua, Cameroon
² Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkey
³ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
⁴ Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

^* e-mail: minc@firat.edu.tr

Received: 13 February 2020
Accepted: 6 April 2020
Published online: 28 April 2020

Abstract

In this paper, exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr nonlinearity form are derived, by adopting two relevant architecture of integration methods namely the extended sinh-Gordon equation expansion method and extended Jacobi elliptic function methods (EJEF method). The studied model, describes the propagation of optical solitons in nonlinear optical fibers. As a results, various types of traveling wave solutions are obtained including Jacobi elliptic function solutions. For some special cases, when the modulus of m approach 0 or 1 it is gained respectively periodic wave solutions and hyperbolic function solutions. Comparing our results with the well-known results in literature are also reported. Lastly the 3D profile to some of the obtained solutions are also plotted.