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[tex]y_{tt}=((y_x)^3)_x+y^3-y[/tex] where y=y(x,t), and we are looking for a solution with a compact support in (-x0,x0) (which I need to find x0), i.e the solution vanishes for x>=x0 or x<=-x0, and also [tex]y=y_x=0[/tex] on the endpoint of the above interval.

Solving the equation by hand is not really a problem, i.e by separation of variables, but plotting the graph of y seems to be a problem for a novice like me in mathematica.

Can anyone help with this problem?

Thanks in advance.