Exact solutions for two nonlinear wave equations with nonlinear terms of any order |
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| Affiliation: | 1. Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada;2. Department of Mathematics, Faculty of Science and Horticulture, Kwantlen Polytechnic University, Surrey, British Columbia V3W 2MB, Canada;3. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, PR China;4. School of Mathematics, University of the Witwatersrand, P Bag 3 Wits, Johannesburg 2050 South Africa;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. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People''s Republic of China;6. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk, Cairo, Egypt;2. Mathematics Department, Faculty of Science and Arts, Taibah University, Al-Ula, Saudi Arabia;3. Mathematics Department, Faculty of Science, Beni-Suef University, Egypt;4. Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh 13318, Saudi Arabia;5. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa |
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| Abstract: | In this paper, based on a variable-coefficient balancing-act method, by means of an appropriate transformation and with the help of Mathematica, we obtain some new types of solitary-wave solutions to the generalized Benjamin–Bona–Mahony (BBM) equation and the generalized Burgers–Fisher (BF) equation with nonlinear terms of any order. These solutions fully cover the various solitary waves of BBM equation and BF equation previously reported. |
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