Open Access

ARTICLE

Application of Modified Extended Tanh Technique for Solving Complex Ginzburg–Landau Equation Considering Kerr Law Nonlinearity

by Yuming Chu^1,2, Muhannad A. Shallal³, Seyed Mehdi Mirhosseini-Alizamini⁴, Hadi Rezazadeh⁵, Shumaila Javeed^6,*, Dumitru Baleanu^7,8

1 Department of Mathematics, Huzhou University, Huzhou, 313000, China
2 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, China
3 Mathematics Department, College of Science, University of Kirkuk, Kirkuk, Iraq
4 Department of Mathematics, Payame Noor University, Tehran, Iran
5 Amol University of Special Modern Technologies, Amol, Iran
6 Department of Mathematics, COMSATS University Islamabad, Chak Shahzad Islamabad, 45550, Pakistan
7 Department of Mathematics, Cankaya University, Ankara, Turkey
8 Institute of Space Sciences, Magurele-Bucharest, Romania

* Corresponding Author: Shumaila Javeed. Email:

Computers, Materials & Continua 2021, 66(2), 1369-1378. https://doi.org/10.32604/cmc.2020.012611

Received 06 July 2020; Accepted 17 July 2020; Issue published 26 November 2020

Abstract

The purpose of this work is to find new soliton solutions of the complex Ginzburg–Landau equation (GLE) with Kerr law non-linearity. The considered equation is an imperative nonlinear partial differential equation (PDE) in the field of physics. The applications of complex GLE can be found in optics, plasma and other related fields. The modified extended tanh technique with Riccati equation is applied to solve the Complex GLE. The results are presented under a suitable choice for the values of parameters. Figures are shown using the three and two-dimensional plots to represent the shape of the solution in real, and imaginary parts in order to discuss the similarities and difference between them. The graphical representation of the results depicts the typical behavior of soliton solutions. The obtained soliton solutions are of different forms, such as, hyperbolic and trigonometric functions. The results presented in this paper are novel and reported first time in the literature. Simulation results establish the validity and applicability of the suggested technique for the complex GLE. The suggested method with symbolic computational software such as, Mathematica and Maple, is proven as an effective way to acquire the soliton solutions of nonlinear partial differential equations (PDEs) as well as complex PDEs.

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