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Singular solitons, shock waves, and other solutions to potential KdV equation

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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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Authors and Affiliations

  1. School of Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Gang-Wei Wang & Tian-Zhou Xu

  2. Faculty of Mathematical Sciences, University of Tabriz, 51666-14766 , Tabriz, Iran

    Ghodrat Ebadi

  3. Department of Mathematical Sciences, Delaware State University, Dover, DE, 19901-2277, USA

    Stephen Johnson, Andre J. Strong & Anjan Biswas

  4. Lake Forest High School, 5407 Killens Pond Road, Felton, DE , 19943, USA

    Stephen Johnson

  5. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    Anjan Biswas

Authors
  1. Gang-Wei Wang
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  2. Tian-Zhou Xu
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  3. Ghodrat Ebadi
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  4. Stephen Johnson
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  5. Andre J. Strong
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  6. Anjan Biswas
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Correspondence to Anjan Biswas.

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Wang, GW., Xu, TZ., Ebadi, G. et al. Singular solitons, shock waves, and other solutions to potential KdV equation. Nonlinear Dyn 76, 1059–1068 (2014). https://doi.org/10.1007/s11071-013-1189-9

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  • DOI: https://doi.org/10.1007/s11071-013-1189-9

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