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

This paper addresses the potential Korteweg–de Vries equation. The singular 1-soliton solution is obtained by the aid of ansatz method. Subsequently, the $$G^{\prime }/G$$G′/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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