Nikan Ahmadi Karchi - School of Mathematics and Computer science, Iran University of Science and Technology, Narmak, Tehran, Iran
Mohammad Bagher Ghaemi - School of Mathematics and Computer science, Iran University of Science and Technology, Narmak, Tehran, Iran
Javad Vahidi - School of Mathematics and Computer science, Iran University of Science and Technology, Narmak, Tehran, Iran

‎This ‎paper ‎adopts‎ the extended rational sinh-cosh as well as sine-cosine procedures to find precise solutions to the Hirota equation and Hirota-Maccari equation‎. ‎It is illustrated that seeking the precise solutions for these equations plays a foremost and effectual role in solving the numerous kinds of PDEs applied in optics, fluid mechanics, plasma physics and solid physics.‎‎ ‎Furthermore‎, ‎we are able to obtain some consequences of dark and cusp wave solutions‎. ‎Besides‎, ‎two-dimensional and three-dimensional surfaces have been drawn in order to acknowledge the concept of the acquired equations‎.

Sine-cosine and sinh-cosh method, Hirota equation, precise solutions‎, ‎Hirota-Maccari ‎system‎