Redundant exact solutions of nonlinear differential equations |
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| Institution: | 1. Novosibirsk State University, Novosibirsk, Russia;2. Institute of Thermophysics SB RAS, Novosibirsk, Russia;3. Lebedev Physical Institute RAS, Moscow, Russia;4. University of Arizona, Tucson, USA;1. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan;2. Hamdard Institute of Information Technology, Hamdard University, Islamabad, Pakistan;3. Department of Electronic Engineering, International Islamic University, Islamabad, Pakistan;4. Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran;1. Firat University, Science Faculty, Department of Mathematics, 23119 Elazig, Turkey;2. Federal University Dutse, Science Faculty, Department of Mathematics, 7156 Jigawa, Nigeria;3. Department of Mathematics, Cankaya University, Ankara, Turkey;4. Institute of Space Sciences, Magurele, Romania;1. College of Sciences and Humanities Studies Al-Kharj, Physics Department, Prince Sattam Bin Abdulaziz University, Al Kharj, Saudi Arabia;2. Research Center for Physics (RCP), Department of Physics, Faculty of Science and Arts, Al-Mikhwah, Al-Baha University, Saudi Arabia;3. Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt;4. Department of Physics, Faculty of Science, Ain Shams University, Cairo, Egypt |
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| Abstract: | We analyze the paper by Wazwaz and Mehanna Wazwaz AM, Mehanna MS. A variety of exact travelling wave solutions for the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation. Appl Math Comput 2010;217:1484–90]. The authors claim that they have found exact solutions of the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation using the tanh–coth method and the Exp-function method. We demonstrate that two of their solutions are incorrect. All the others can be simplified and they are the partial cases of the well-known solution. Wazwaz and Mehanna made a number of typical mistakes in finding exact solutions of nonlinear differential equations. Taking the results of this paper we introduce the definition of redundant exact solutions for the nonlinear ordinary differential equations. |
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