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CountourPlot W(U) enter image description here I have this following code of it:

eps1 = 2;
eps2 = 1.5;
n = 0;
\[Delta] = 1/2 (1 - eps2/eps1);

ContourPlot[
 Evaluate[{(D[BesselJ[n, U], 
         U]/(BesselJ[n, U] * U) + (1 - 2*\[Delta])/W  * 
        D[BesselK[n, W], W]/(BesselK[n, W] ))*
     (D[BesselJ[n, U], U]/(BesselJ[n, U] * U) + 
       1/W  * D[BesselK[n, W], W]/(BesselK[n, W] )) ==  0}], {U, 1, 
  10}, {W, 1, 9}, WorkingPrecision -> 10, FrameLabel -> Automatic, 
 PlotLegends -> Automatic, PlotPoints -> 150]

but I need to plot as following V(U), where V=Sqrt(U^2+W^2)

If I put W = Sqrt[V^2 - U^2] in eq like this:

ContourPlot[
 Evaluate[{(D[BesselJ[n, U], 
         U]/(BesselJ[n, U] * U) + (1 - 2*\[Delta])/Sqrt[V^2 - U^2]  * 
        D[BesselK[n, Sqrt[V^2 - U^2]], 
          Sqrt[V^2 - U^2]]/(BesselK[n, Sqrt[V^2 - U^2]] ))*
     (D[BesselJ[n, U], U]/(BesselJ[n, U] * U) + 
       1/Sqrt[V^2 - U^2]  * 
        D[BesselK[n, Sqrt[V^2 - U^2]], 
          Sqrt[V^2 - U^2]]/(BesselK[n, Sqrt[V^2 - U^2]] )) ==  
    0}], {U, 1, 10}, {V, 1, 15}, WorkingPrecision -> 10, 
 FrameLabel -> Automatic, PlotLegends -> Automatic, PlotPoints -> 150]

I'll get this picture, where is nothing... enter image description here I actually don't understand, how to do it. Pls help

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6
  • $\begingroup$ Use ParametricPlot? Can you expand on your problem a bit more and add some context? $\endgroup$
    – MarcoB
    Jun 21 at 21:07
  • 1
    $\begingroup$ Just substitute in the expression that you are plotting that $W=\pm\sqrt{V^2-U^2}$ taking care the sign. $\endgroup$
    – yarchik
    Jun 21 at 21:22
  • $\begingroup$ @yarchik, this way doesn't help $\endgroup$
    – Albert
    Jun 21 at 22:19
  • $\begingroup$ @MarcoB, ok I added some more information $\endgroup$
    – Albert
    Jun 21 at 22:20
  • $\begingroup$ D[BesselK[n, Sqrt[V^2 - U^2]], Sqrt[V^2 - U^2]] is incorrect code, as Mathematica states whey it is executed. Instead, try D[BesselK[n, z], z] /. z -> Sqrt[V^2 - U^2]. $\endgroup$
    – bbgodfrey
    Jun 21 at 22:34

1 Answer 1

6
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Use ContourPlot3D for U^2+W^2==V^2 and f[U,V] as MeshFunction sine the plot is the intersection of U^2+W^2==V^2 and f[U,V]==0.

Clear[f];
eps1 = 2;
eps2 = 1.5;
n = 0;
δ = 1/2 (1 - eps2/eps1);
f[U_, W_] = (D[BesselJ[n, U], U]/(BesselJ[n, U]*U) + (1 - 2*δ)/
       W*D[BesselK[n, W], W]/(BesselK[n, W]))*(D[BesselJ[n, U], 
       U]/(BesselJ[n, U]*U) + 1/W*D[BesselK[n, W], W]/(BesselK[n, W]));
ContourPlot3D[U^2 + W^2 == V^2, {U, 0, 10}, {V, -10, 10}, {W, 0, 10}, 
 MeshFunctions -> Function[{U, V, W}, f[U, W] // Evaluate], 
 Mesh -> {{0}}, MeshStyle -> Red, ContourStyle -> None, 
 ViewProjection -> "Orthographic", ViewPoint -> {0, 0, 1}, 
 BoundaryStyle -> None, AxesLabel -> {"U", "V", None}, 
 Ticks -> {Automatic, Automatic, None}, PlotPoints -> 150, 
 MaxRecursion -> 4]

enter image description here

The same as ( We use {V, U, 10} in order to set V>U)

ContourPlot[
 f[U, W] == 0 /. W -> Sqrt[V^2 - U^2] // Evaluate, {U, 0, 10}, {V, U, 
  10}, PlotPoints -> 150, MaxRecursion -> 4]

enter image description here

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