Construction of periodic and solitary wave solutions by the extended Jacobi elliptic function expansion method |
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| Affiliation: | 1. Department of Mathematics, Beijing Jiao Tong University, Beijing 100044, China;2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China;3. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;4. School of Mathematics, South China University of Technology, Guangzhou 510640, China;5. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA;6. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China;7. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa |
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| Abstract: | In this paper, an extended Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the exact periodic solutions of some polynomials or nonlinear evolution equations. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in nonlinear mathematical physics. As a result, many exact travelling wave solutions are obtained which include new solitary or shock wave solution and envelope solitary and shock wave solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics. |
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