janhardo

@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 ...

Answered: janhardo 690

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...

Answered: janhardo 690

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...

Answered: janhardo 690

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...

Answered: janhardo 690

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 ....

Answered: janhardo 690

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]);

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]);

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]);

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;

>

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

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

Answered: janhardo 690

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]);

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]);

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 ...

Answered: janhardo 690

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

@salim-barzani I dealt with your fi...

Answered: janhardo 690

February 23 2025

0 0

@salim-barzani
I dealt with your first lump pdf example and haven't looked at the other lump examples yet.
Don't know what the urgency is for your calculations?
Maybe you can do something with it, as physically you have more knowledge of it than me.
When I look at the later examples of pdf lumps you have given they are all lumps moving on a straight line
Maybe these examples have even better information ?

@salim-barzani I stay at this examp...

Answered: janhardo 690

February 23 2025

0 0

@salim-barzani
I stay at this example all the time : Question How find line for plotting ? i
I do not separate my code ,its all related to this example
Now i found a trajectory for the pdf example 1-lumps and probably for the other lumps too, because they are all straight lines

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positions of the 1 lump waves...

@salim-barzani &....

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

@salim-barzani ...

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

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

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

@salim-barzani ....

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

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