New exact solutions to the CDF equations |
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| Authors: | Teoman Özer |
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| Institution: | 1. Centre for Undergraduate Studies, University of the Punjab, Lahore 54590, Pakistan;2. Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan;1. Department of Mathematics and Computer Science, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran;2. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa;1. Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000 Annaba, Algeria;2. Faculty of Electronic Engineering, Department of Telecommunications, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia;3. Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA;4. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 80203, Saudi Arabia |
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| Abstract: | New exact soliton solutions to the Cologero–Degasperies–Fokas (CDF) equations in (1+1)-dimension and (2+1)-dimension by using the improved tanh method are investigated. First, the (1+1)-dimensional CDF equation is analyzed. By the improved tanh method, the corresponding nonlinear partial differential equation is reduced to the nonlinear ordinary differential equations and then the different types of exact solutions to the original equation are obtained based on the solutions of the Riccati equation. For the case of (2+1)-dimensional CDF equation the same computation procedure is carried out. It is presented that one could obtain new exact explicit solutions, which are traveling wave solutions, to (2+1)-dimensional CDF equation. Additionally, some graphical representations of the solitary and periodic solutions are presented. |
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