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Seven common errors in finding exact solutions of nonlinear differential equations
Authors:Nikolai A Kudryashov
Institution:1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-7500, USA;2. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey;5. Institute of Physics Belgrade, Pregrevica 118, 11080 Zemun, Serbia;1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762, USA;2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. Department of Mathematics, Faculty of Arts and Sciences, Uludag University, 16059 Bursa, Turkey;5. Department of Mathematics, Howard University, Washington, DC 20059, USA;6. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People''s Republic of China;7. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt;2. Department of Mathematics, College of Science, Taif University, P.O.BOX 11099, Taif 21944, Saudi Arabia;1. Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Muscat, Oman;2. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762 7500, United States;3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;4. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, PR China;5. Gulf University, Communication and Networks Engineering, Bahrain
Abstract:We analyze the common errors of the recent papers in which the solitary wave solutions of nonlinear differential equations are presented. Seven common errors are formulated and classified. These errors are illustrated by using multiple examples of the common errors from the recent publications. We show that many popular methods in finding the exact solutions are equivalent each other. We demonstrate that some authors look for the solitary wave solutions of nonlinear ordinary differential equations and do not take into account the well - known general solutions of these equations. We illustrate several cases when authors present some functions for describing solutions but do not use arbitrary constants. As this fact takes place the redundant solutions of differential equations are found. A few examples of incorrect solutions by some authors are presented. Several other errors in finding the exact solutions of nonlinear differential equations are also discussed.
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