Compare Mathematica with MATLAB by plotting the same equation

Questions
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1

Firstly, the MATLAB programme is

t = 0;
A = 2;
c1 = 1;
c2 = 1;
c = 1/25;
omega = 2;

[xi,eta]=meshgrid(-5:0.1:5,-4:0.1:6);

P = ((2*sinh(xi+omega*t))./(3*cosh(xi+omega*t)))+((5*sinh(xi+omega*t))./(6*cosh(xi+omega*t)).^3)+0.9;
Q = -(sinh(eta))./(cosh(eta));
x = xi-2.5*tanh(xi+omega*t);
y = eta;

Px = -(sech(xi+omega*t)).^2;
Qy = -(sech(eta)).^2;

u = ((A-c1.*c2).*Px.*Qy)./(1+c1.*P+c2.*Q+c.*P.*Q).^2;
view([-45 70]);

surf(x,y,u);
xlabel('x','FontSize',26,'FontName','Times New Roman','FontAngle', 'italic')
ylabel('y','FontSize',26,'FontName','Times New Roman','FontAngle', 'italic')
zlabel('$u$','interpreter','latex','FontSize',24,'FontName','Times New Roman','FontAngle', 'italic')

and it comes

MATLAB.png
MATLAB.png576×514 48.1 KB

With the same equation, the Mathematica program is

\[Omega] = 2;
A = 2; Subscript[c, 1] = Subscript[c, 2] = 1; Subscript[c, 3] = 1/25;
px = -Sech[\[Xi] + \[Omega] t]^2; p = (2 Sinh[\[Xi] + \[Omega] t])/(
  3 Cosh[\[Xi] + \[Omega] t]) + (5 Sinh[\[Xi] + \[Omega] t])/(
  6 Cosh[\[Xi] + \[Omega] t]^3) + 0.9;
qy = -Sech[\[Eta]]^2; q = -(Sinh[\[Eta]]/Cosh[\[Eta]]);
func[\[Xi]_, \[Eta]_, 
   t_] = ((A - Subscript[c, 1] Subscript[c, 2]) px qy)/(1 + 
      Subscript[c, 1] p + Subscript[c, 2] q + Subscript[c, 3] p q)^2 //
     Rationalize // Simplify;
xyToXiEta[x_, y_, t_] := 
  NSolve[{x == \[Xi] - 2.5 Tanh[\[Xi] + 2 t], 
    y == \[Eta]}, {\[Xi], \[Eta]}, Reals];
With[{t = 0}, 
 ListPlot3D[
  Flatten[Table[{x, y, func[\[Xi], \[Eta], t]} /. 
     xyToXiEta[x, y, t], {x, -2, 2, 0.04}, {y, -1, 5, 0.04}], 2], 
  Axes -> True, PlotRange -> {All, All, {0, 2}}, 
  AxesLabel -> {x, y, z}, ColorFunction -> "TemperatureMap"]]

and it comes

MMA.png
MMA.png451×276 28.7 KB

Thanks Gianluca Gorni for providing the Mathematica program.

It is obvious that the MATLAB picture forms like a bridge with empty space under it. However, the Mathematica picture is solid.

How can I improve the Mathematica program to make it like MATLAB’s result?

MATLAB.m (676 Bytes)
MMA.nb (5.57 KB)

2

A direct translation of the code is not possible as that function does not exist (ListParametricPlot3D or so). But we can recreate the graphic “manually” by recreating the polygons, or rewrite the code to use ParametricPlot3D (preferred and nicer), I included both:

Open in Wolfram Cloud ↗
3

Thank you for your reply. It is an excellent answer.

4

Cross-posted in https://mathematica.stackexchange.com/q/261847/1871

Please include the link(s) of other version(s) of your question when cross-posting to avoid repetive work.

5

Thank you for your notification, I will pay attention to this matter.

6

It is much easier to bypass x,y and plot directly with respect to xi,eta:

With[{t = 0}, 
 With[{x = \[Xi] - 2.5 Tanh[\[Xi] + 2 t], y = \[Eta]}, 
  ParametricPlot3D[{x, y, func[\[Xi], \[Eta], t]}, {\[Xi], -1, 
    2}, {\[Eta], -1, 4}, PlotRange -> All, 
   ColorFunction -> "TemperatureMap"]]]
7

Thank you for your reply.