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Shallow water waves model in coefficient PDE or general PDE

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Dear All,
I want to solve the Shallow water waves equation in PDE module in 2D. h is the water elevation.

How can I implement an incoming pulse in the times domain from the left on the structure.

If I use the initial conditions, I can specify the shape at given time but I don t see any way of defining for example a incoming wave from the left to the right with a shape like:
h(x,y,t)=exp((t-t0)^2)sin(2*pi*freqt)

Best regards
Muamer

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