Asian Research Journal of Mathematics 8(3): 1-13, 2018; Article no.ARJOM.36887 ISSN: 2456-477X _____________________________________ *Corresponding author: E-mail: m.elhobaty@zu.edu.ly; The Solitary Travelling Wave Solutions of Some Nonlinear Partial Differential Equations Using the Modified Extended Tanh Function Method with Riccati Equation M. M. El-Horbaty 1,2* and F. M. Ahmed 2 1 Department of Mathematics, Faculty of Science, Zagazig University, Egypt. 2 Department of Mathematics, Faculty of Science, Alegelat , Zawia University, Libya. Authors’ contributions This work was carried out in collaboration between both authors. Both authors read and approved the final manuscript. Article Information DOI: 10.9734/ARJOM/2018/36887 Editor(s): (1) Nikolaos Dimitriou Bagis, Department of Informatics and Mathematics, Aristotelian University of Thessaloniki, Greece. Reviewers: (1) Grienggrai Rajchakit, Maejo University, Thailand. (2) Md. Abdus Salam, Mawlana Bhashani Science and Technology University, Bangladesh. Complete Peer review History: http://www.sciencedomain.org/review-history/22934 Received: 21 st September 2017 Accepted: 16 th January 2018 Published: 30 th January 2018 _______________________________________________________________________________ Abstract In this work, we aimed to construct a variety of solitary travelling wave solutions of a wide class of nonlinear partial differential equations (PDE's) that is governed by a presented single nonlinear partial differential equation (PDE) using the powerful modified extended Tanh method with Riccati equation. More general solutions are successfully constructed including the previous known formal solutions such as shock wave, periodic and weirstrass solutions. Keywords: Modified Extended Tanh; Riccati equation; solitary wave solutions; nonlinear PDE’s. 1 Introduction Nonlinear partial differential equations (PDE's) have a major importance in the field of nonlinear physical phenomena such as plasma physics, optical fibers, solid state physics, fluid mechanics and other branches of science, most of these equations are nonlinear and difficult to handle due to the nonlinearity term(s). In Original Research Article