plotting – How to have a 3d plot of a complex polynomial?


I’m trying to have a 3d plot for a complex polynomial using the ContourPlot3D It shows me a plot which does not vary when the input values of different variables are varied. So, I guess it is just a dummy plot I’m getting. Kindly guide me as how to get a correct 3d plot. I’m using Mathematica version 9.

omegaJ = (0.41*10^-5)^-1; 
lambdaJ = 1.724*10^15; 
n0 = 10^12;
zion = 1.602*10^-19;
e = 1.602*10^-19;

t0 = 10^6;
melec = 9.1094*10^-31;
Subscript(ν, i) = 1.00*10^1;
Subscript(ν, id) = 5.00*10^-3;
Subscript(ν, ed) = 1.00*10^2;
rdust = 37.5*10^-6;

telec = 2.6*10^4;
tion = .26*10^4;
temp = telec;

mion = 2*10^-14;
mnd = 4.0*10^-16;

grav = 6.67*10^-11;
veff = 10;
nion = 2*10^5;
η = 0.01;
cs = Sqrt(telec/mion)*(4*π*n0*mion*grav)^-0.5;

Subscript(n, e0) = 5*10^3;
Subscript(n, i0) = 10^3;
Subscript(ϕ, g) = -2.51*temp/e;
Subscript(q, d0) = rdust*Subscript(ϕ, g);

Subscript(I, e0) = 
   Abs(-π*rdust^2*e*Sqrt(((8*telec)/(π*melec)))*Subscript(n, e0) * Exp((e*Subscript(q, d0))/(rdust*telec)));
Subscript(I, i0) = Abs(π*rdust^2*e*Sqrt(((8*tion)/(π*mion)))*Subscript(n, i0)*
Exp(1 - (e*Subscript(q, d0))/(rdust*tion)));
Subscript(ν, ndch) = 10^4*e;

SuperStar(c) = (-Subscript(ν, ed) + Subscript(ν, i) - 2*n0*veff)/omegaJ;

SuperStar(d) = ((3*η*omegaJ)/(
              melec*n0*lambdaJ*ξ^2)) + ((η*omegaJ*k^2)/(
                melec*n0*lambdaJ));

SuperStar(q) = (4*π*e^2*n0*lambdaJ^2)/telec ; 
a4 = telec/(mion*cs^2);
r1 = zion*(2*veff*n0 - Subscript(ν, i));
r2 = - telec*(1/(melec*lambdaJ) + (Subscript(q, d0)*omegaJ)/(e*mnd));
r3 = (2*t0*k)/(melec*lambdaJ);
r4 = a4*zion*omegaJ;
r5 = a4*Subscript(I, i0)*omegaJ;

p1 = SuperStar(c)*SuperStar(d)*SuperStar(
q)*(e*r4*Subscript(ν, ndch) + r5) ; 
p2 = (cs*Subscript(ν, ndch)*e*r4 - SuperStar(c)*cs*omegaJ*e*r4 + SuperStar(d)*e*r4 + cs*r5)*omegaJ*SuperStar(q) ; 
p3 = (e*r1*Subscript(ν, ndch) + 
Subscript(I, e0)*Subscript(ν, id) + r1*Subscript(I, i0)) * SuperStar(q)*r2 ; 
p4 = SuperStar(c)*SuperStar(d)*Subscript(ν, ndch)*Subscript(ν, id)*e;
p5 = (cs*Subscript(ν, ndch)*Subscript(ν, id) + 
SuperStar(d)*Subscript(ν, id) - 
SuperStar(c)*cs*omegaJ*Subscript(ν, id) + 
SuperStar(d)*Subscript(ν, ndch) - 
SuperStar(c)*cs*omegaJ*Subscript(ν, ndch) - 
SuperStar(c)*SuperStar(d)*omegaJ)*e*
omegaJ ; 
p6 = -cs*e*omegaJ^3 ; 
q1 = (SuperStar(d)*Subscript(ν, ndch)*e*r4 - 
SuperStar(c)*cs*omegaJ*Subscript(ν, ndch)*e*r4 - 
omegaJ*SuperStar(c)*SuperStar(d)*e*r4 + SuperStar(d)*r5 - 
SuperStar(c)*cs*omegaJ*r5)*SuperStar(q) ; 
q2 = -cs*omegaJ^2*e*r4*SuperStar(q) ; 
q3 = (e*r1 + Subscript(I, e0))*omegaJ*r2*SuperStar(q);
q4 = (SuperStar(d)*Subscript(ν, ndch)*Subscript(ν, id) - 
       SuperStar(c)*cs*omegaJ*Subscript(ν, ndch)*Subscript(ν, 
          id) - SuperStar(c)*SuperStar(d)*omegaJ*Subscript(ν, id) - 
            SuperStar(c)*SuperStar(d)*omegaJ*Subscript(ν, ndch))*e;
              q5 = -(cs*Subscript(ν, id) + cs*Subscript(ν, ndch) + 
                SuperStar(d) - SuperStar(c)*cs*omegaJ)*e*omegaJ^2;

(* Roots *)

y - (p1 + (p4 - p3)*(1/ξ - I k))/(q1 + (q3 + q4)*(1/ξ - I k)) == 0;
x == 0;


(* Plot *)
ContourPlot3D(y, {y, 0, 10}, {ξ, 0.01, 10}, {k, 1, 100}, 
  PlotLegends -> {"y", "ξ", "k"}, AxesLabel -> {"y", "ξ", "k"},
  PlotLegends -> Automatic, Mesh -> None, 
  ContourStyle -> Directive(Red, Opacity(0.8), Specularity(White, 30)))

η = 0.03;

y - (p1 + (p4 - p3)*(1/ξ - I k))/(q1 + (q3 + q4)*(1/ξ - I k)) == 0;
ContourPlot3D(y, {y, 0, 10}, {ξ, 0.01, 10}, {k, 1, 100}, 
  PlotLegends -> {"y", "ξ", "k"}, AxesLabel -> {"y", "ξ", "k"},
  PlotLegends -> Automatic, Mesh -> None, 
  ContourStyle -> Directive(Red, Opacity(0.8), Specularity(White, 30)))

η = 0.05;

y - (p1 + (p4 - p3)*(1/ξ - I k))/(q1 + (q3 + q4)*(1/ξ - I k)) == 0;
ContourPlot3D(y, {y, 0, 10}, {ξ, 0.01, 10}, {k, 1, 100}, 
  PlotLegends -> {"y", "ξ", "k"}, AxesLabel -> {"y", "ξ", "k"},
  PlotLegends -> Automatic, Mesh -> None, 
  ContourStyle -> Directive(Red, Opacity(0.8), Specularity(White, 30)))

mnd = 5.0*10^-16;

y - (p1 + (p4 - p3)*(1/ξ - I k))/(q1 + (q3 + q4)*(1/ξ - I k)) == 0;
ContourPlot3D(y, {y, 0, 10}, {ξ, 0.01, 10}, {k, 1, 100}, 
  PlotLegends -> {"y", "ξ", "k"}, AxesLabel -> {"y", "ξ", "k"},
  PlotLegends -> Automatic, Mesh -> None, 
  ContourStyle -> Directive(Red, Opacity(0.8), Specularity(White, 30)))