unmatched output for density plot

Question

I am plotting Abs[R] on y-axis vs k on x-axis with the following code

ϖ = -2 Cos[κ];
α = 1;
Subscript[V, 0] = -2.5;
ε = 0.05;
μ = 0.3;
  Subscript[V, 1] = Subscript[V, 0] (1 + ε);
  Subscript[V, 2] = Subscript[V, 0] (1 - ε);
  Subscript[δ, 2] = 
  Subscript[V, 2] - ϖ + (α*(Abs[R]))/(
  1 + μ*(Abs[R]));
  Subscript[δ, 1] = 
  Subscript[V, 
  1] - ϖ + (α*(Abs[R])*(1 - 
  2 Subscript[δ, 2]*Cos[κ] + Subscript[δ, 
  2]^2))/(1 + μ*(Abs[R])*(1 - 
   2 Subscript[δ, 2]*Cos[κ] + Subscript[δ, 
   2]^2)) ;
 χ = -κ;
 Subscript[ζ, 2] = 
 Subscript[V, 1] - ϖ + (α*(Abs[R]))/(
 1 + μ*(Abs[R]));
Subscript[ζ, 1] = 
Subscript[V, 
2] - ϖ + (α*(Abs[R])*(1 - 
  2 Subscript[ζ, 2]*Cos[χ] + Subscript[ζ, 
  2]^2))/(1 + μ*(Abs[R])*(1 - 
   2 Subscript[ζ, 2]*Cos[χ] + Subscript[ζ, 2]^2))
;

Then the plot command

g1 = DensityPlot[{(Abs[(E^(I κ) - 
       E^(-I κ))/(1 + (Subscript[δ, 1] - E^(
          I κ)) (E^(I κ) - Subscript[δ, 
          2]))]^2 - 
   Abs[(E^(I χ) - 
       E^(-I χ))/(1 + (Subscript[ζ, 1] - E^(
          I χ)) (E^(I χ) - Subscript[ζ, 
          2]))]^2)/(Abs[(E^(I κ) - 
       E^(-I κ))/(1 + (Subscript[δ, 1] - E^(
          I κ)) (E^(I κ) - Subscript[δ, 
          2]))]^2 + 
   Abs[(E^(I χ) - 
       E^(-I χ))/(1 + (Subscript[ζ, 1] - E^(
          I χ)) (E^(I χ) - Subscript[ζ, 
          2]))]^2)} /. {Abs[R] -> x}, {κ, 0, π}, {x, 0,
10}, ColorFunction -> ColorData["SolarColors"], PlotPoints -> 200,
  PlotRange -> All, AspectRatio -> 21/27, ImageSize -> 272, 
  Frame -> True, Axes -> True, 
  FrameLabel -> {κ, Style[Abs[R]^2, 21]}, 
  FrameStyle -> Directive[Black, FontSize -> 18], 
  FrameTicks -> {{{0, 2, 4, 6, 8, 10}, None}, {{0, 1, 2, 3}, None}}]

I get an output which I believe is close to the desired one, but due to the wrong choice of colors (maybe) i can not match mine with the following which is the desired output, Can someone please help change the ColorFunction, so that I can get as close to the desired as possible. The required output with legend is

Answer 1

This is how you can overcome this problem: You can get the pixel values corresponding to the function from legend picture like:

data = {{0, 0, 0}, {77, 0, 0}, {149, 0, 0}, {231, 0, 0}, {255, 60, 0}, {255, 135, 0}, {255, 222, 0}, {255, 255, 42}, {255, 255, 118}, {255, 254, 187}, {255, 255, 255}};,

than you can interpolate, rescaling the doman from {-1,1} to {0,1} (because it seems that ColorFunction clips the values to be positive) :

f = Interpolation[Transpose[{Range[0, 1, 0.1], 1/255. (data)}], x]; colorfunc[x_] = RGBColor[f];

and then plot your function with additional options:

g1 = DensityPlot[{(Abs[(E^(I κ) - E^(-I κ))/(1 + (Subscript[δ, 1] - E^( I κ)) (E^(I κ) - Subscript[δ, 2]))]^2 - Abs[(E^(I χ) - E^(-I χ))/(1 + (Subscript[ζ, 1] - E^( I χ)) (E^(I χ) - Subscript[ζ, 2]))]^2)/(Abs[(E^(I κ) - E^(-I κ))/(1 + (Subscript[δ, 1] - E^( I κ)) (E^(I κ) - Subscript[δ, 2]))]^2 + Abs[(E^(I χ) - E^(-I χ))/(1 + (Subscript[ζ, 1] - E^( I χ)) (E^(I χ) - Subscript[ζ, 2]))]^2)} /. {Abs[R] -> x}, {κ, 0, π}, {x, 0, 10}, PlotPoints -> 200, PlotRange -> All, AspectRatio -> 21/27, ImageSize -> 272, ColorFunction -> colorfunc, PlotLegends -> Automatic, Frame -> True, Axes -> True, FrameLabel -> {κ, Style[Abs[R]^2, 21]}, FrameStyle -> Directive[Black, FontSize -> 18], FrameTicks -> {{{0, 2, 4, 6, 8, 10}, None}, {{0, 1, 2, 3}, None}}].

I get this:

BTW, it seems like the function that you are plotting is a bit different from the image.