Eur. Phys. J. Plus (2020) 135: 313
https://doi.org/10.1140/epjp/s13360-020-00296-w

Regular Article

New exact solutions for nematicons in liquid crystals by the -expansion method arising in fluid mechanics

¹ Department of Mathematics, Faculty of Education, Erciyes University, 38039, Melikgazi, Kayseri, Turkey
² Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
³ Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran
⁴ Department of Mechanical Engineering, College of Engineering, University of Zakho, Zakho, Iraq
⁵ Department of Mathematics and Science Education, Faculty of Education, Harran University, Şanlıurfa, Turkey

^* e-mail: oailhan@erciyes.edu.tr

Received: 30 October 2019
Accepted: 21 February 2020
Published online: 16 March 2020

Abstract

In this research paper, we try to illustrate the structure of the novel exact soliton wave solutions of nematicons in liquid crystals with four law nonlinearity forms including the Kerr, power, parabolic and dual-power by utilizing the -expansion method. The aim of this research is not just to find the dark, bright, combined dark-bright, singular types, traveling and solitary solutions of nematicons in liquid crystals by investigating the aforementioned method, showing the differences between the obtained solutions and other solutions obtained by using different methods. Moreover, constraints guarantee the existence of the obtained solutions. Eventually, we believe that the enforced method is more powerful and efficient than other methods and the obtained solutions in this paper can help us to understand soliton molecules in liquid crystals. That will be extensively used to describe many interesting physical phenomena in the areas of gas, plasma, optics, acoustics, fluid dynamics, classical mechanics and so on.