How should I define the boundary and initial conditions in NDSolve...?

Questions
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1

How should I define the boundary and initial conditions in NDSolve for the following partial differential equation?

See attached word document for code and error messages

I want the output to be a 3D surface that is shaped by the boundary and initial conditions, but I am having trouble with defining them in a way that will evaluate.

What I have for the I.C.s and B.C.s so far comes from an example given in the help menu for NDSolve where the “Nonlinear sine-Gordon equation in two spatial dimensions with periodic boundary conditions” is evaluated. While I expect this is not the right direction, it seemed to serve as a decent starting point.

Thanks in advance for the help!

2

Please do not put word document as attachment. If the code is too long, why not post the actual notebook as attachment? How is one going to run Microsoft word inside Mathematica?

3

Vincent,

specify t. Note that your solution does not exist on the entire {t, 0, 10} interval.

Try Manipulate[ Plot3D[Evaluate[z[x, y, t] /. sol], {x, -Pi, Pi}, {y, -Pi, Pi}, PlotRange -> All], {t, 0, 5.27}]

Peter