All exact travelling wave solutions of Hirota equation and Hirota–Maccari system

• Published in: Optik (Stuttgart) Vol. 127; no. 4; pp. 1848 - 1859
• Main Authors: Tuluce Demiray, Seyma, Pandir, Yusuf, Bulut, Hasan
• Format: Journal Article
• Language: English
• Published: Elsevier GmbH 01-02-2016
• Subjects: Extended trial equation method; Generalized Kudryashov method; Hirota equation; Hirota–Maccari system; Travelling wave solution; Hirota equation; Generalized Kudryashov method; Hirota–Maccari system; Extended trial equation method; Travelling wave solution
• ISSN: 0030-4026; 1618-1336
• DOI: 10.1016/j.ijleo.2015.10.235

Modelling of wave motion and propagation characteristics of waves plays an important role in coastal, ocean and maritime engineering, and for most geographical areas, waves are the major source of environmental actions on beaches or on man-made fixed or floating structures. The travelling wave solutions are described by the hyperbolic functions, the trigonometric functions and the rational functions. In this paper, exact travelling wave solutions of Hirota equation and Hirota–Maccari system are successfully surveyed. Extended trial equation method and generalized Kudryashov method are applied to gain some exact travelling wave solutions of Hirota equation and Hirota–Maccari system. Firstly, we find some exact travelling wave solutions of Hirota equation and Hirota–Maccari system with the aid of extended trial equation method. Secondly, we obtain dark soliton solutions of Hirota equation and Hirota–Maccari system by means of generalized Kudryashov method. Finally, for certain parameter values, we plot two and three dimensional graphics of imaginary and real values of some solutions that we obtained by using these methods.