A110818 Coefficient (times -1) of the 1/r^(2n) term in the radial far-field expansion of the squared amplitude of a unit topological point charge (-1 or +1 vortex) in the two-dimensional Ginzburg-Landau equation.

1, 2, 19, 374, 12559, 645992, 47367124, 4701142286, 607384076311, 99104140036610, 19933965307701547, 4846421980399770152, 1401149529610562030404, 475128611089824908724944, 186768400411319414544569368, 84248002219370115308687582078

Offset

1,2

Comments

Ginzburg-Landau vortex solutions are fundamental in the study of superconductors and superfluids.

Links

Table of n, a(n) for n=1..16.

María 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

Cf. A111100.

Sequence in context: A308330 A078369 A090308 * A325288 A155927 A353290

Adjacent sequences: A110815 A110816 A110817 * A110819 A110820 A110821

Keyword

nonn

Author

Greg Huber, Sep 15 2005

Extensions

Terms a(13) and beyond from Andrey Zabolotskiy, Aug 04 2023

Status

approved