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Singular solitons,shock waves,and other solutions to potential KdV equation |
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| Authors: | Gang-Wei Wang Tian-Zhou Xu Ghodrat Ebadi Stephen Johnson Andre J. Strong Anjan Biswas |
| Affiliation: | 1. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China 2. Faculty of Mathematical Sciences, University of Tabriz, 51666-14766?, Tabriz, Iran 3. Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA 4. Lake Forest High School, 5407 Killens Pond Road, Felton, DE?, 19943, USA 5. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia |
| Abstract: | This paper addresses the potential Korteweg–de Vries equation. The singular 1-soliton solution is obtained by the aid of ansatz method. Subsequently, the $G^{prime }/G$ -expansion method and the exp-function approach also gives a few more interesting solutions. Finally, the Lie symmetry analysis leads to another plethora of solution to the equation. These results are going to be extremely useful and applicable in applied mathematics and theoretical physics. |
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