New sets of solitary wave solutions to the KdV,mKdV, and the generalized KdV equations |
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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 work we introduce new schemes, each combines two hyperbolic functions, to study the KdV, mKdV, and the generalized KdV equations. It is shown that this class of equations gives conventional solitons and periodic solutions. We also show that the proposed schemes develop sets of entirely new solitary wave solutions in addition to the traditional solutions. The analysis can be used to a wide class of nonlinear evolutions equations. |
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