How to plot solution of a 2D edp on a 1D line

I would like to plot the solution of 2D edp on a line using for instance gnuplot.
How can I get this done?

More generally I would like to plot solution on a given contour.
How can I define this contour and interpolate the solution on points lying on this contour.

Thanks for help

Hello Christophe,
Probably this example or that one can help you achieve what you want?

Hi Pierre, Thanks example 1 is perfect.