@Kitonum 
Thanks 

with(Optimization);
[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, 

  NLPSolve, QPSolve]

Minimize(419*x^2 + 116*x*y - 426*x*z + 78*y^2 - 142*y*z + 133*z^2 - 1604*x - 682*y + 1086*z + 2306);
       [0., [x = 7.00000000000007, y = 11.0000000000001, 

         z = 13.0000000000002]]

Seems to be not strict symbolic ?

@salim-barzani 
Is this function for the 3 plots on different times ?
"can you plot by Ai you have lets see how many shape you have ?"   what are shapes ?

2*((t*(-alpha*conjugate(lambda[1] + lambda[2]*I)^3 + b*conjugate(lambda[1] + lambda[2]*I) + c*r[2] + a) + 2*beta*(y*conjugate(lambda[1] + lambda[2]*I) + z*r[2] + x))/(2*beta) + (t*(-alpha*(lambda[1] + lambda[2]*I)^3 + b*(lambda[1] + lambda[2]*I) + c*r[1] + a) + 2*beta*(y*(lambda[1] + lambda[2]*I) + z*r[1] + x))/(2*beta))/(((t*(-alpha*(lambda[1] + lambda[2]*I)^3 + b*(lambda[1] + lambda[2]*I) + c*r[1] + a) + 2*beta*(y*(lambda[1] + lambda[2]*I) + z*r[1] + x))*(t*(-alpha*conjugate(lambda[1] + lambda[2]*I)^3 + b*conjugate(lambda[1] + lambda[2]*I) + c*r[2] + a) + 2*beta*(y*conjugate(lambda[1] + lambda[2]*I) + z*r[2] + x)))/(4*beta^2) - 4/((lambda[1] + lambda[2]*I - conjugate(lambda[1] + lambda[2]*I))^2*alpha))

@salim-barzani 

That resembles a normal 3D plot at u= 0 , where you see peaks and a density plot at level -1.

Is that possible?

@salim-barzani 
conjugate_functie_voorschriftmprimes25-9-2025.mw

@salim-barzani 

It seems to be incorrect in Maple to use direct index variables (such as Lambda) in an arrow operator function.(Line -1-Done)

It is possible to do so indirectly, as shown in the plot example.

"how many graph and hsape of design you can make it?"      hsape ?

The z= 0 is only for creating a contour plot over the x-y plane of the lumps. ?

@salim-barzani 
? 
trajectory_lump_vraag_mprimes_25-9-2025.mw

@acer Thanks

This seems the shortest solution. 

eq := B12 = -6*(p1 + p2)/(p1 - p2)^2;
F2 := (theta1*theta2*p1^2 + (-2*p2*theta1*theta2 - 6)*p1 + theta1*theta2*p2^2 - 6*p2)/(p1 - p2)^2;


simplify(F2, {eq}, [p1, p2]);

@acer Thanks, I am sorry.

I should have said simplify both expressions into a new expression until the new desired expression appears.

@acer 

Thanks, but we're too focused on achieving a certain expression.

Should I just start with F2 and B12 and do something with that?

Strange, not wanted outcome 
yes, or no ?

The situation is that there is F2 and B12 expressions, and is there a simplification possible ?

@sand15 
Thanks ,  it has become more complicated than I had anticipated

@salim-barzani 
What is the bilinear pde derived from your original pde you posted?
From there to get a tau function and applying the longwave limiet for a lump ( f4) 

@salim-barzani 
I haven't done anything yet with the given PDE to derive a Hiroto bilinear form.
And then, from there, set up the tau function.
Didn't I create a procedure (corrected existing procedure) for that bilinear form to obtain it easily?
Remember that this procedure does not accept an integral expression in the PDE, so the procedure is of no use here for this 2sdk PDE.

I did start with an assumed (known?) tau function to obtain the F4 expression, but the desired form has not yet been achieved without errors, as can be seen in the code, so...

@salim-barzani 
The tau function for F4 has been accepted and is not yet symbolically derived?