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On nonlinear differential equation with exact solutions having various pole orders
Institution: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. Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P. O. Box 12, 23000 Annaba, Algeria;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. 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. Department of Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran;2. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran;3. Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA;4. Faculty of Science, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Abstract:We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed.
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