Question: Numerical solution of the "fractal-like" Ginzburg-Landau equation


I would like to find the numerical solution of the Ginzburg-Landau equation for the1D, written in the form 

(diff(z(x), x, x))*kappa^2-(1-d)*kappa^2*(diff(z(x), x))/x+z(x)-z(x)^3 = 0

For d=1 and with the boundary conditions z(-infinity)=0 and z(infinity)=1 the solution is well-known, this is tanh(x) function.

My goal is to undertand the evolution of the numerical solution for the interval of the dimensionality 0<d<1. However, I faced with the problem that even for d=1 (the classical case) I get the error "Error, (in dsolve/numeric/bvp) Newton iteration is not converging".

Here is my simple code



R0 := (diff(z(x), x, x))*kappa^2-(1-d)*kappa^2*(diff(z(x), x))/x+z(x)-z(x)^3;

kappa := 2; d := 1;

p := dsolve({R0, z(-15) = 0, z(15) = 1}, type = numeric, range = -15 .. 15, maxmesh = 50000):


Thank you in advance.

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