Eur. Phys. J. Plus (2019) 134: 20
https://doi.org/10.1140/epjp/i2019-12442-4

Regular Article

New complex waves in nonlinear optics based on the complex Ginzburg-Landau equation with Kerr law nonlinearity

¹ Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
² Department of Mathematics, Duba University College, University of Tabuk, Tabuk, Saudi Arabia
³ Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran
⁴ Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida, Porto, Portugal

^* e-mail: mofatzi@sci.cu.edu.eg

Received: 28 August 2018
Accepted: 30 November 2018
Published online: 14 January 2019

Abstract

A variety of new complex waves representing solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity is investigated. Two different approaches are used, namely the generalized exponential function and the unified methods. Complex periodic, solitary, soliton, and elliptic wave solutions of phenomena that occur in nonlinear optics or in plasma physics are obtained. The physical meaning of the geometrical structures for some solutions is discussed for different choices of the free parameters. It is shown that the proposed methods lead to powerful mathematical tools for obtaining the exact traveling wave solutions of complex nonlinear evolution equations.