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janhardo

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@salim-barzani  your question is ab...

janhardo 715
February 24 2025
0 0

@salim-barzani 
your question is about the 2 lump wave ....

@salim-barzani  "is about add ...

janhardo 715
February 24 2025
0 0

@salim-barzani 
"is about add to line for and 2 y finction with a[1]a[2]b[1]b[2] inside of y[1] and y[2]"
I don't know what exactly you mean by this ?
explain this more 

@salim-barzani  ...

janhardo 715
February 24 2025
0 0

@salim-barzani 

@salim-barzani I am trying to creat...

janhardo 715
February 24 2025
0 0

@salim-barzani 

I am trying to create a a procedure that can handle  a dynamic contour plot.

@salim-barzani  What happened then?...

janhardo 715
February 24 2025
0 0

@salim-barzani 
What happened then?

positions of the 1 lump waves...

janhardo 715
February 23 2025
0 0

positions of the 1 lump waves 

@salim-barzani    &....

janhardo 715
February 23 2025
0 0

@salim-barzani 

@salim-barzani  I read a comment ju...

janhardo 715
February 23 2025
0 0

@salim-barzani 
I read a comment just now from the 2 lump wave function that time : t , useful to study the dynamic behaviour  
Have not looked at the 1 lump wave at the role that : t can play
There is a t in this function ??

@salim-barzani    ...

janhardo 715
February 23 2025
0 0

@salim-barzani 


 

> 

 

> 

 

> 

restart;
with(plots):

# Parameters
alpha := 1: beta := 1:
l3 := -1 - 2*I: l3_conj := -1 + 2*I:
l4 := -2/3 - I: l4_conj := -2/3 + I:

# Theta functions
theta := (x,y,t,l) -> x + l*y - (alpha + beta/l)*t:

# Corrected B_ij terms
B := (li, lj) -> 3*(li + lj)/(beta*(li - lj)^2):

# Construct f(x,y,t)
f := (x,y,t) -> simplify(expand(
    theta(x,y,t,l3)*theta(x,y,t,l3_conj)*theta(x,y,t,l4)*theta(x,y,t,l4_conj)
    + B(l3,l3_conj)*theta(x,y,t,l4)*theta(x,y,t,l4_conj)
    + B(l3,l4)*theta(x,y,t,l3_conj)*theta(x,y,t,l4_conj)
    + B(l3,l4_conj)*theta(x,y,t,l3_conj)*theta(x,y,t,l4)
    + B(l3_conj,l4)*theta(x,y,t,l3)*theta(x,y,t,l4_conj)
    + B(l3_conj,l4_conj)*theta(x,y,t,l3)*theta(x,y,t,l4)
    + B(l4,l4_conj)*theta(x,y,t,l3)*theta(x,y,t,l3_conj)
    + B(l3,l3_conj)*B(l4,l4_conj)
    + B(l3,l4)*B(l3_conj,l4_conj)
    + B(l3,l4_conj)*B(l3_conj,l4)
)):

# Corrected lump solution using second x-derivative
u := (x,y,t) -> 12*(diff(f(x,y,t), x$2))/(f(x,y,t))^2 - 12*(diff(f(x,y,t), x)^2)/(f(x,y,t))^3:

# Generate the contour plot
contourplot(Re(u(x,y,0)), x = -30..30, y = -30..30, contours=40, grid=[300,300],
    coloring=[blue,white,red], title="2-Lump Wave (t=0)", labels=["x","y"]);

plot3d(Re(u(x,y,0)), x=-30..30, y=-30..30, grid=[200,200], style=surface,
       shading=zhue, axes=boxed, labels=["x","y","u"],
       title="3D plot 2-Lump Wave (t=0)");

 

 

this is the example for the 2 lump wave  for example 1 information
  ... 1 lump wave
  ... 2 lump wave
becomes too difficult to express this 2 lump wave like for the 1 lump wave ?

> 

 

> 

 

info to add

 
> 

 

verification example

 
> 

> 

 

> 

 

> 

 


 

Download 2_-lump_wave_plot_23-2-2025_mprimes.mw

@salim-barzaniProblem here is to keep fo...

janhardo 715
February 23 2025
0 0

@salim-barzani
Problem here is to keep following example 1 for the 2 lumps solution lying on different lines to compare with the approach for the 1 lumps lying on 1 line.
That approach can try to use again, but now I don't know because information is missing ? 
Is there any more information for the example 1 with a 1 lump and 2 lump and 3 lump and M lump solutions examples.

@salim-barzani By deriving one, two...

janhardo 715
February 23 2025
0 0

@salim-barzani 
By deriving one, two , three lumps for the example on one line   , there shows another expression his excistence ?




 

@salim-barzaniI stay all the time to the...

janhardo 715
February 23 2025
0 0

@salim-barzani
I stay all the time to the first example, all expessions are from that intended  

x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;
x2 := 0;   y2 := -1/3*x2 - sqrt(30)/6;
x3 := 40;  y3 := -1/3*x3 - sqrt(30)/6;
they number but why write like that? have any information? can be any number? 


"also in paper mention the time variable t? but in here we don't have a t? and this is you done is a new thing by my openion if i am not wrong?"

The 1 lumps are positioned along the straight line  , at time t= 0 there is no lump , but there is a velocity  for the lump ?
S = V* t 
The 3 lump positions are on the line : choosen ?

 

 

@salim-barzani   ....

janhardo 715
February 23 2025
0 0

@salim-barzani 

> 

restart;
with(plots):

a := 1;
b := 2;

# Lump posities
x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;
x2 := 0;   y2 := -1/3*x2 - sqrt(30)/6;
x3 := 40;  y3 := -1/3*x3 - sqrt(30)/6;

# Bewegingslijn
eq := y = -1/3*x - sqrt(30)/6;

# Lump soliton functie
U := (x, y, a, b) -> 12*(-b^4*y^2 + (a*y + x)^2*b^2 - 3*a^2) /
                     (b^4*y^2 + (a*y + x)^2*b^2 + 3*a^2)^2;

# Drie afzonderlijke contourplots voor elke lump, elk met een andere kleur
contour1 := contourplot(U(x - x1, y - y1, a, b), x = -50 .. 50, y = -30 .. 30,
                        contours = 30, color = red, grid = [100, 100], transparency = 0.1):

contour2 := contourplot(U(x - x2, y - y2, a, b), x = -50 .. 50, y = -30 .. 30,
                        contours = 30, color = blue, grid = [100, 100], transparency = 0.1):

contour3 := contourplot(U(x - x3, y - y3, a, b), x = -50 .. 50, y = -30 .. 30,
                        contours = 30, color = green, grid = [100, 100], transparency = 0.1):

# Bewegingslijn
trajectory_plot := implicitplot(eq, x = -50 .. 50, y = -30 .. 30, color = black, thickness = 2):

# Alles samenvoegen
display(contour1, contour2, contour3, trajectory_plot,
        title = "3-Lump Soliton met Bewegings Trajectorie",
        labels = ["x", "y"], scaling = constrained, size = [1200, 800]);

1

  

2

  

-40

  

40/3-(1/6)*30^(1/2)

  

0

  

-(1/6)*30^(1/2)

  

40

  

-40/3-(1/6)*30^(1/2)

  

y = -(1/3)*x-(1/6)*30^(1/2)

  

proc (x, y, a, b) options operator, arrow; 12*(-b^4*y^2+(a*y+x)^2*b^2-3*a^2)/(b^4*y^2+(a*y+x)^2*b^2+3*a^2)^2 end proc

  

 
> 

restart;
with(plots):

a := 1;
b := 2;

# Lump posities
x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;
x2 := 0;   y2 := -1/3*x2 - sqrt(30)/6;
x3 := 40;  y3 := -1/3*x3 - sqrt(30)/6;

# Bewegingslijn
eq := y = -1/3*x - sqrt(30)/6;

# Lump soliton functie
U := (x, y, a, b) -> 12*(-b^4*y^2 + (a*y + x)^2*b^2 - 3*a^2) /
                     (b^4*y^2 + (a*y + x)^2*b^2 + 3*a^2)^2;

# Drie afzonderlijke contourplots voor elke lump
contour1 := contourplot(U(x - x1, y - y1, a, b), x = -50 .. 50, y = -30 .. 30,
                        contours = 50, color = red, grid = [100, 100], transparency = 0.2):
contour2 := contourplot(U(x - x2, y - y2, a, b), x = -50 .. 50, y = -30 .. 30,
                        contours = 50, color = blue, grid = [100, 100], transparency = 0.2):
contour3 := contourplot(U(x - x3, y - y3, a, b), x = -50 .. 50, y = -30 .. 30,
                        contours = 50, color = green, grid = [100, 100], transparency = 0.2):

# Bewegingslijn
trajectory_plot := implicitplot(eq, x = -50 .. 50, y = -30 .. 30, color = black, thickness = 2):

# Alles samenvoegen
display(contour1, contour2, contour3, trajectory_plot,
        title = "3-Lump Soliton met Bewegings Trajectorie",
        labels = ["x", "y"], scaling = constrained, size = [1200, 800]);

1

  

2

  

-40

  

40/3-(1/6)*30^(1/2)

  

0

  

-(1/6)*30^(1/2)

  

40

  

-40/3-(1/6)*30^(1/2)

  

y = -(1/3)*x-(1/6)*30^(1/2)

  

proc (x, y, a, b) options operator, arrow; 12*(-b^4*y^2+(a*y+x)^2*b^2-3*a^2)/(b^4*y^2+(a*y+x)^2*b^2+3*a^2)^2 end proc

  

 
> 

restart;
with(plots):

a := 1;
b := 2;

# Lump posities
x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;
x2 := 0;   y2 := -1/3*x2 - sqrt(30)/6;
x3 := 40;  y3 := -1/3*x3 - sqrt(30)/6;

# Bewegingslijn
eq := y = -1/3*x - sqrt(30)/6;

# Lump soliton functie
U := (x, y, a, b) -> 12*(-b^4*y^2 + (a*y + x)^2*b^2 - 3*a^2) /
                     (b^4*y^2 + (a*y + x)^2*b^2 + 3*a^2)^2;

# Superpositie van alle drie lumps in ÉÉN enkele functie
U_total := (x, y) -> U(x - x1, y - y1, a, b) +
                     U(x - x2, y - y2, a, b) +
                     U(x - x3, y - y3, a, b);

# Contourplot met een aangepaste kleurenfunctie voor onderscheid
contour_lumps := contourplot(U_total(x, y),
    x = -50 .. 50, y = -30 .. 30, contours = 50,
    coloring = [red, blue, green], grid = [100, 100],
    filled = true, size = [1200, 800]
):

# Bewegingslijn toevoegen
trajectory_plot := implicitplot(eq, x = -50 .. 50, y = -30 .. 30,
                                color = black, thickness = 2):

# Weergeven van de volledige plot
display(contour_lumps, trajectory_plot,
        title = "3-Lump Soliton met Bewegings Trajectorie",
        labels = ["x", "y"], scaling = constrained, size = [1200, 800]);

1

  

2

  

-40

  

40/3-(1/6)*30^(1/2)

  

0

  

-(1/6)*30^(1/2)

  

40

  

-40/3-(1/6)*30^(1/2)

  

y = -(1/3)*x-(1/6)*30^(1/2)

  

proc (x, y, a, b) options operator, arrow; 12*(-b^4*y^2+(a*y+x)^2*b^2-3*a^2)/(b^4*y^2+(a*y+x)^2*b^2+3*a^2)^2 end proc

  

proc (x, y) options operator, arrow; U(x-x1, y-y1, a, b)+U(x-x2, y-y2, a, b)+U(x-x3, y-y3, a, b) end proc

  

 
> 

restart;
> 

 


 

Download 3_1_d_lumps_samen_getekend-23-2-2025_part_B_mprimes_.mw

@salim-barzani  I made some lump pl...

janhardo 715
February 23 2025
0 0

@salim-barzani 
I made some lump plots, but with the colered ones ,it seems that the lumps are not equal .. lol


 

> 

restart;
with(plots):
> 

 

> 

a := 1;
b := 2;

# Lump posities overgenomen uit de afbeelding
x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;
x2 := 0;   y2 := -1/3*x2 - sqrt(30)/6;
x3 := 40;  y3 := -1/3*x3 - sqrt(30)/6;

# Bewegingslijn
eq := y = -1/3*x - sqrt(30)/6;

# Lump soliton functie
U := (x, y, a, b) -> 12*(-b^4*y^2 + (a*y + x)^2*b^2 - 3*a^2) /
                     (b^4*y^2 + (a*y + x)^2*b^2 + 3*a^2)^2;

# Contour plot met alle drie lumps en verschillende kleuren
contour_lumps := contourplot(
    U(x - x1, y - y1, a, b) + U(x - x2, y - y2, a, b) + U(x - x3, y - y3, a, b),
    x = -50 .. 50, y = -30 .. 30, contours = 230,
    coloring = [red, blue, green], grid = [100, 100], size = [1200, 800]
):

# Bewegingslijn
trajectory_plot := implicitplot(eq, x = -50 .. 50, y = -30 .. 30, color = blue, thickness = 2):

# Toon alles in één enkele grote plot
display(contour_lumps, trajectory_plot,
        title = "3-Lump Soliton met Bewegings Trajectorie", labels = ["x", "y"], scaling = constrained, size = [1200, 800]);

1

  

2

  

-40

  

40/3-(1/6)*30^(1/2)

  

0

  

-(1/6)*30^(1/2)

  

40

  

-40/3-(1/6)*30^(1/2)

  

y = -(1/3)*x-(1/6)*30^(1/2)

  

proc (x, y, a, b) options operator, arrow; 12*(-b^4*y^2+(a*y+x)^2*b^2-3*a^2)/(b^4*y^2+(a*y+x)^2*b^2+3*a^2)^2 end proc

  

 
> 

a := 1;
b := 2;

# Lump posities correct overgenomen uit de afbeelding
x1 := -40; y1 := -1/3*x1 - sqrt(30)/6;
x2 := 0;   y2 := -1/3*x2 - sqrt(30)/6;
x3 := 40;  y3 := -1/3*x3 - sqrt(30)/6;

# Bewegingslijn
eq := y = -1/3*x - sqrt(30)/6;

# Lump soliton functie
U := (x, y, a, b) -> 12*(-b^4*y^2 + (a*y + x)^2*b^2 - 3*a^2) /
                     (b^4*y^2 + (a*y + x)^2*b^2 + 3*a^2)^2;

# Contour plots met verschillende kleuren per lump
contour_1 := contourplot(U(x - x1, y - y1, a, b), x = -50 .. 50, y = -30 .. 30,
                          contours = 200, coloring = [red, white, blue], grid = [100, 100]):

contour_2 := contourplot(U(x - x2, y - y2, a, b), x = -50 .. 50, y = -30 .. 30,
                          contours = 200, coloring = [green, white, purple], grid = [100, 100]):

contour_3 := contourplot(U(x - x3, y - y3, a, b), x = -50 .. 50, y = -30 .. 30,
                          contours = 200, coloring = [cyan, white, orange], grid = [100, 100]):

# Bewegingslijn
trajectory_plot := implicitplot(eq, x = -50 .. 50, y = -30 .. 30, color = black, thickness = 4):

# Alles samenvoegen in één enkele grote plot
display(contour_1, contour_2, contour_3, trajectory_plot,
        title = "3-Lump Soliton met Bewegings Trajectorie", labels = ["x", "y"], scaling = constrained. size = [1000, 600]);

1

  

2

  

-40

  

40/3-(1/6)*30^(1/2)

  

0

  

-(1/6)*30^(1/2)

  

40

  

-40/3-(1/6)*30^(1/2)

  

y = -(1/3)*x-(1/6)*30^(1/2)

  

proc (x, y, a, b) options operator, arrow; 12*(-b^4*y^2+(a*y+x)^2*b^2-3*a^2)/(b^4*y^2+(a*y+x)^2*b^2+3*a^2)^2 end proc

  

 
> 

 

> 

 


 

Download 3_1_d_lumps_samen_getekend-23-2-2025_mprimes_.mw

 

@salim-barzani    ...

janhardo 715
February 23 2025
0 0

@salim-barzani 

 

> 

restart;
with(plots):

# Definieer de lump-oplossing (gecorrigeerde haakjes)
U := (x, y, a, b) -> 12*(-b^4*y^2 + (a*y + x)^2*b^2 - 3*a^2) / ((b^4*y^2 + (a*y + x)^2*b^2 + 3*a^2)^2);

# Kies parameters (bijv. a = 1, b = 1)
a := 1:
b := 1:

# Plot de lump
lump_plot := plot3d(U(x, y, a, b), x = -5..5, y = -5..5, axes = framed, style = surfacecontour):

# Plot de rechte baan x + a*y = 0 als een 3D-lijn
pathline_plot := spacecurve([-a*y, y, 0], y = -5..5, color = red, thickness = 3):

# Combineer beide plots
display({lump_plot, pathline_plot});

proc (x, y, a, b) options operator, arrow; 12*(-b^4*y^2+(a*y+x)^2*b^2-3*a^2)/(b^4*y^2+(a*y+x)^2*b^2+3*a^2)^2 end proc

  

 
> 

 


 

Download 1_d_lump_getekend_met_bewegindslijn23-2-2025mprimes_.mw

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