Torrential forced KdV equation : Soliton solutions over a hole

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Abstract Torrential flow of an incompressible and a perfect fluid over a hole is investigated in infinite channel, with a focus on the steady case of the governed equation. The flow is supposed to be two-dimensional and irrotational. The problem studied here included just the influence of the gravity $g$ and the surface-tension effects are neglected. The issue has been programed and run on a computer to solve a nonlinear ordinary differential equation of the third order, called the forced Korteweg de Vries equation. The obtained results in the torrential flow, have been represented graphically by varying the shape of the hole, its cavity, and also the value of the Froude number λ.

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