OFFSET
1,2
COMMENTS
Ginzburg-Landau vortex solutions are fundamental in the study of superconductors and superfluids.
LINKS
MarÃa Aguareles Carrero, Interaction of spiral waves in the general complex Ginzburg-Landau equation, Universitat Politècnica de Catalunya, Doctoral thesis, 2007. See Eqs. (1.11)-(1.13).
EXAMPLE
a(3) = 19 because A(r)^2 = 1 - 1/r^2 - 2/r^4 - 19/r^6 - ...
MATHEMATICA
n = 17;
v = 1; (* change to 2 to get A111100 *)
sol = AsymptoticDSolveValue[{4 z^3 f''[z] + 4 z^2 f'[z] - f[z] v^2 z + (1 - f[z]^2) f[z] == 0, f[0] == 1}, f[z], {z, 0, n}];
Rest@CoefficientList[1 - sol^2 + O[z]^n, z] (* Andrey Zabolotskiy, Aug 04 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Greg Huber, Sep 15 2005
EXTENSIONS
Terms a(13) and beyond from Andrey Zabolotskiy, Aug 04 2023
STATUS
approved