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Jun 25, 2013 at 3:02 review First posts
Jun 25, 2013 at 11:08
Jun 19, 2013 at 22:34 comment added user35122 Thanks Jon, I did check & as it turns out, the f(V)=V solution doesn't converge in the torus. The source f(V)/R^2 (interpreting the equation as Poisson's equation) needs to go to zero eventually. So any finite series for f(V) is out of the question. I guess that's it.
Jun 18, 2013 at 6:38 comment added Jon For $n=1$ this is a linear PDE and it appears a Schroedinger-like equation with a $\frac{1}{R^2}$ potential. One must verify that the zero eigenvalue does occur.
Jun 15, 2013 at 5:55 comment added Alex Patterson Thanks - we'll keep going with numerical methods. But one more question: does anyone notice a clever choice of f(V) to yield a specific solution?
Jun 14, 2013 at 20:29 comment added Carlo Beenakker this is a nonlinear Poisson equation --- there's no algebraic solution, you'll have to resort to numerics. math.uiowa.edu/ftp/atkinson/nonlinear_poisson.pdf
Jun 14, 2013 at 19:35 history asked Alex Patterson CC BY-SA 3.0