On the nontrivial non-travelling wave profiles of nonlinear evolution and wave equations |
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| Authors: | Yaliang Shen Yueping Zhu Nanbin Cao |
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| Institution: | 1. School of Science, Nantong University, Nantong, Jiangsu 226007, PR China;2. School of Science, Shijiazhuang University of Economics, Shijiazhuang, Hebei 050031, PR China;3. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China;1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China;2. Department of Mathematics, University of Texas-Rio Grande Valley, Edinburg, TX 78539, USA;1. Pusan National University, Mathematics Department, Busan, 609-735, Republic of Korea;2. Iowa State University, Mathematics Department, Ames, IA 50011, United States |
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| Abstract: | The overall aim of the present paper is to find and analyze the new non-travelling wave solutions of the nonlinear evolution and wave equations. With the aid of symbolic computation and based on the generalized extended tanh-function method, we propose the newly extended tanh-function expansion algorithm and get many new non-travelling wave solutions of the (2 + 1)-dimensional Broer–Kaup–Kupershmidt equations. The solutions which we obtain are more abundant than the solutions which the generalized extended tanh-function method gets. At the same time, the solutions contain arbitrary functions which may be helpful to explain some complex phenomena. We also give some figures to describe the property of these solutions. In additions, the method can also be successfully applied to other nonlinear evolution and wave equations. |
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