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For example, I have this plot below - I want to be able to fade (opacity) of lines based upon a function of x and xi

     ClearAll["Global`*"]; xi = 2; k0 = 5; \[Sigma] = 2;
 Show[Table[
   sol = NDSolve[{D[x[t], 
        t] == (Sinh[(\[Sigma]^2) x[t] (t - xi)])/(Cos[2 k0 x[t]]), 
      x[0] == n}, x[t], {t, -4, 8}];
   ParametricPlot[{t, x[t]} /. sol, {t, 0, 8}, PlotRange -> All, 
    BaseStyle -> Thick, AxesStyle -> Thickness[.001], 
    LabelStyle -> {Black, Medium}, ColorFunctionScaling -> False, 
    ColorFunction -> 
     Function[{x, y, t}, 
      Directive[
       Opacity[.05 + (E^(-(1/2) (x - xi)^2 \[Sigma]^2) Sqrt[\[Pi]/
        2] \[Sigma] (1 + E^(2 x (-xi) \[Sigma]^2))) /. sol[[1]] //
          First], Blue]]], {n, -1, 3 - 1/4, 1/4}]]

Any help would be great - thank you.

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  • $\begingroup$ I have made a better example of what I want here mathematica.stackexchange.com/questions/174547/… $\endgroup$ – Betty Jun 4 '18 at 2:53
  • $\begingroup$ Why didn't the answer you got to your previous not work? What is different here that the previous answer doesn't cover this question? $\endgroup$ – m_goldberg Jun 10 '18 at 0:57