# Plot implicit function with intermediate variable

Cross-posted in Wolfram Community.

Here, I intend to plot a 3D picture of

with two implicit functions

where $$x, y, t, \xi, \eta$$, are variables. Of course, these variables can be constrained to certain interval that will guarantee the function to be well-posed. My code is attached below.

How can I draw this one?

x == ξ - 0.5 Tanh[ξ - 0.3 t] - Tanh[ξ - 0.1 t] -
1.5 Tanh[ξ + 0.1 t];

y == η - 1.5 Tanh[η];

Plot3D[-((
1350. Sech[η]^2 Tanh[η] (1. Sech[0.1 t - ξ]^2 Tanh[
0.1 t - ξ] +
0.6 Sech[0.3 t - ξ]^2 Tanh[0.3 t - ξ] +
1.6 Sech[0.1 t + ξ]^2 Tanh[0.1 t + ξ]))/((1 -
1.5 Sech[η]^2) (1 - Sech[0.1 t - ξ]^2 -
0.5 Sech[0.3 t - ξ]^2 -
1.5 Sech[0.1 t + ξ]^2) (0.3 Sech[η]^2 +
0.5 Sech[0.1 t - ξ]^2 + 0.3 Sech[0.3 t - ξ]^2 -
0.8 Sech[0.1 t + ξ]^2)^2)), {x, -12, 12}, {y, -12, 12},
AxesLabel -> {Style[x, Medium], Style[y, Medium]}]

• Many issues with your syntax. Your == statements are not assignment statements; they are boolean statements: x and y will not be assigned a value. Your Plot3D is not a function of x and y so nothing will plot. Jan 9 at 4:29
• Thank you for your reply. However, even ==" is replaced by =", it can not work too. Here, x == ξ - 0.5 Tanh[ξ - 0.3 t] - Tanh[ξ - 0.1 t] - 1.5 Tanh[ξ + 0.1 t]; y == η - 1.5 Tanh[η];'' means two constrains, particualy. Jan 9 at 5:01
• As @Edmund said, the function you are trying to plot is a function of t, ξ and η and not x and y. This means that unless they are in turn functions of x and y you cannot plot them as a function ofx and y. In order to give a 3D plot you would also need to fix one of the variables i.e. t, or ξ` . Jan 9 at 6:24
• It is exactly the point that \xi and \eta can not be solved analytically, which cause the problem. Jan 9 at 7:28
• Jan 9 at 13:32