Eur. Phys. J. Plus (2018) 133: 189
https://doi.org/10.1140/epjp/i2018-12020-4

Regular Article

A new approach to exact optical soliton solutions for the nonlinear Schrödinger equation

¹ Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria, Chilpancingo, Guerrero, Mexico
² CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
³ Cankaya University, Faculty of Art and Sciences, Department of Mathematics, Balgat 0630, Ankara, Turkey
⁴ Institute of Space Sciences, P.O.BOX, MG-23, R 76900, Magurele-Bucharest, Romania

^* e-mail: jgomez@cenidet.edu.mx

Received: 21 February 2018
Accepted: 16 April 2018
Published online: 18 May 2018

Abstract

By using the modified homotopy analysis transform method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving a new fractional conformable derivative in the Liouville-Caputo sense and the fractional-order derivative with the Mittag-Leffler law. Employing theoretical parameters, we present some numerical simulations and compare the solutions obtained.