Give ai the right results ?

@Aixleft math 
 

Download 9-3-2025-How_to_verify_set_A_and_set_B_is_equivalent_mprimes_def.mw

Download 9-3_-2025_complex_functie_3d_plot_mprimes_.mw

@SSMB 

It also has nothing to do with your assignments in my opinion
By the looks of it, Maple does not succeed in calculating symbolic equilibrium points of the complex function, that leaves numerical ?.

@FZ 
Now with hyperbolic and trigionometric functions the expression becomes larger 

Download vraag_mprimes_7-3-2025veeenvoudig_lineaire_algebra.mw

Download afleiding_oplossing_pde_Klein-Gordon_equation_2-3-2025_mprimes.mw

Unfortunately,  not yet been able to get a dynamically generated timestamp for a 2 lump wave soliton in a contour plot.
However, adjustable axes are possible in the procedure
 The further the 2-lumps evolve in time , it seems like they become 1 lump solitons ?  


 

Download 2-_lump_wave_assenbereik_2-3-2025_mprimes.mw

could be correct, checking time positions


 

" i want do it without textplot in the file tester" 
I am sorry  i don't know yet a solution for text  and is different coding than for a 1 lump soliton.
I must try out different methods ..

@Arya-S-AA 
 

restart;
with(plots):

a := -1;
b := -2;
alpha := 1;
beta := 1;
vx := -3/5;
vy := 1/5;
trajectory_slope := vy/vx;
x0 := 0;
y0 := trajectory_slope*x0;

U := (x, y, t, a, b, alpha, beta) -> 4*beta*((y*a - 2*alpha*t + x)*b^2 + a*(-2*beta*t + a*(y*a - 2*alpha*t + x))*b^2)/
(-b^6*beta*y^2 + (-4*t*y*beta^2 + (-2*a^2*y^2 + (4*alpha*t - 2*x)*a*y - 4*(alpha*t - 1/2*x)^2)*beta + 3*a)*b^4 + 
(-4*t^2*beta^3 + 4*a*t*(y*a - 2*alpha*t + x)*beta^2 - a^2*(y*a - 2*alpha*t + x)^2*beta + 6*a^3)*b^2 + 3*a^5);

MultiLumpPlot := proc(tijden::list, kleuren::list, custom_grid::list := [500, 500]) 
    local contourplots, tijd, pos_shift, xmin, xmax, ymin, ymax, trajectory_plot, text_labels, all_plots, i; 
    
    contourplots := []; 
    text_labels := []; 
    
    if nops(tijden) <> nops(kleuren) then 
        error "Het aantal kleuren moet gelijk zijn aan het aantal tijdstippen."; 
    end if; 
    
    xmin := infinity; xmax := -infinity; 
    ymin := infinity; ymax := -infinity; 
    
    for i to nops(tijden) do 
        tijd := tijden[i]; 
        pos_shift := [x0 + vx*tijd, y0 + vy*tijd]; 
        
        xmin := min(xmin, pos_shift[1] - 30); 
        xmax := max(xmax, pos_shift[1] + 30); 
        ymin := min(ymin, pos_shift[2] - 30); 
        ymax := max(ymax, pos_shift[2] + 30); 
        
        contourplots := [op(contourplots), 
            contourplot(eval(U(x - pos_shift[1], y - pos_shift[2], 0, a, b, alpha, beta)), 
                        x = xmin .. xmax, y = ymin .. ymax, 
                        contours = 40, color = kleuren[i], grid = custom_grid, transparency = 0.05)];
        
        text_labels := [op(text_labels), 
            textplot([pos_shift[1], pos_shift[2] + 3, cat("t=", round(tijd)), 
            'font' = ["Arial", 12, 'bold']])];  # Hier wordt tijd afgerond
    end do; 
    
    trajectory_plot := implicitplot(y = trajectory_slope*x, x = xmin .. xmax, y = ymin .. ymax, color = black, thickness = 2); 
    
    all_plots := display(op(contourplots), trajectory_plot, op(text_labels), 
                         title = "1-Lump Soliton waves", 
                         labels = ["x", "y"], scaling = constrained, 
                         view = [xmin .. xmax, ymin .. ymax]); 
    
    return all_plots; 
end proc:

MultiLumpPlot([-100, 200, 0, 100], ["blue", "green", "purple", "red"], [100, 100]);    

@Arya-S-AA 
This is a 1 lump soliton code :from line-with-t-test.mw
What exactly do you want to write down in this plot ?
Note : the title of the plot should be corrected to 1-lump soliton

@salim-barzani 
I don't know what the availability is worIdwide for the two ai platforms ?
I use a paid chatgpt of 20 usd per month.  

@salim-barzani 
i did already, but you remove this information on th eforum

@Arya-S-AA 

Becomes already a trickier task to plot a fourth 2-lump soliton at t= 100
A procedure that will randomly draw numbers of 2 -lump wave at a given time is even more complicated

 

restart:
with(plots):
with(PDEtools):
declare(u(x, y, t), quiet);

# ✅ Parameters
a[1] := -1: b[1] := -2:
a[2] := -2/3: b[2] := -1:
a[3] := -4/5: b[3] := -3/2:  # Extra lump toegevoegd
alpha := 1: beta := 1:
vx := -3/5: vy := 1/5:

# ✅ Tijdstippen per 2-lump soliton
t1 := -50:  # Tijdstip voor eerste soliton
t2 := 0:    # Tijdstip voor tweede soliton
t3 := 50:   # Tijdstip voor derde soliton

# ✅ 2-lump wave functie
u_expr := -2*((9/65 - 18*I/65)*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x)*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x) + (9/65 + 18*I/65)*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x) + (7933424/1891125 + 36508832*I/1891125)*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x) + (6/65 + 9*I/65)*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x) + (6/65 - 9*I/65)*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x)*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x) + (8059833/1092650 - 84073113*I/2185300)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x) + (7933424/1891125 - 36508832*I/1891125)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x) + (8059833/1092650 + 84073113*I/2185300)*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x))/(9*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x)*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x)/65 + (27783/1625 - 11619*I/1625)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x) + 135*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x)/52 + (74331/109265 + 118467*I/109265)*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x) + (74331/109265 - 118467*I/109265)*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x)*((-2/3 + I)*t + (5/9 + 4*I/3)*y + t + (2/3 - I)*x) + 26*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x)*((-1 + 2*I)*t + (3 + 4*I)*y + t + (1 - 2*I)*x)/45 + (27783/1625 + 11619*I/1625)*(-(1 + 2*I)*t + (3 - 4*I)*y + t + (1 + 2*I)*x)*(-(2/3 + I)*t + (5/9 - 4*I/3)*y + t + (2/3 + I)*x) + 126229597/50430):

# ✅ Contourplots voor de drie tijdstippen
contour1 := contourplot(eval(u_expr, t = t1), x = -200..200, y = -100..100, contours = 30, color = red):
contour2 := contourplot(eval(u_expr, t = t2), x = -200..200, y = -100..100, contours = 30, color = green):
contour3 := contourplot(eval(u_expr, t = t3), x = -200..200, y = -100..100, contours = 30, color = blue):

# ✅ Tijdsaanduiding op de figuur
time_labels := textplot([[0, 50, cat("t=", t1)], [0, 0, cat("t=", t2)], [0, -50, cat("t=", t3)]], font=["Arial", 12, 'bold']):

# ✅ Combineer de plots
display(contour1, contour2, contour3, time_labels, labels = ["x", "y"], title="Drie 2-Lump Solitons bij Verschillende Tijdstippen", scaling=constrained);

@Arya-S-AA 
A procedure can also be made for the ‘2 lump waves’ I think with time indications?