A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations |
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| 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 Science and Arts, Bozok University, 66100 Yozgat, Turkey;5. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran;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. Institute of Mathematics, Humboldt University of Berlin, Rudower Chaussee 25, D-12489 Berlin, Germany;2. Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova St. 3b, 79060 Lviv, Ukraine |
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| Abstract: | A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer–Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations. |
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