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salim-barzani

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1 years, 16 days
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don't waste time...

salim-barzani 1560
December 26 2024
0 0

@janhardo they are unchangable 

this is my first time i asked this...

salim-barzani 1560
December 26 2024
0 0

@mmcdara I’m not sure why they did that, and I think I’ve deleted all my previous posts about this because of them also hirota operator. That aside, I thought the graph should look like this in 2D—the middle one. 

question?...

salim-barzani 1560
December 25 2024
0 0

@mmcdara How i can plot 2D of this data? it will show effect of noise?

reply...

salim-barzani 1560
December 25 2024
0 0

@mmcdara 

Thank you so much for providing the code and for your effort! I truly appreciate your help. I have a few questions regarding the implementation:

  1. What happens to the W(t)W(t)W(t) function in the code? You’ve initialized it as w(t)=0w(t) = 0w(t)=0, but is this just the initial condition?

  2. In the line STX := TX_Wfree *~ T_W;, what does this operation mean conceptually?

  3. How can I modify the matrix to include additional data, such as adding a new column?

  4. I’d like to improve the design and visual clarity of the plot directly within the program, without using external tools. I need these plots for my paper and would like to include labels for the axes, specifying whether they represent absolute, real, or imaginary values for each graph. Additionally, is it possible to generate 2D plots for each graph of the STX matrix?

Your assistance is invaluable, and it will significantly enhance my work. I’ll always remember your support and contribution.

 

reply...

salim-barzani 1560
December 25 2024
0 0

@nm  i posted the same in mathematica someone at there answered then i read the paper at one place he mention that . and effect of noise he not shown in graph i don't know what is w(t) at his graph 

reply...

salim-barzani 1560
December 25 2024
0 0

@nm  when epsilon= +&- 1 the answer satisfy

reply...

salim-barzani 1560
December 25 2024
0 0

@nm  thanks for your efort, i did al step as he did in paper i have different method for solving but for skeching graph i must sketch same graph as he did to figure out what is w(t) in him solution function ,in this graph sigma(delta) is zero but in other graph sigma  is not zero and if you watch graph is contain range of x, 
note(W(t)) is brawnian motion) or wiener process, but at all i can't see effect of this function in graph of paper at all


 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

with(Physics)
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(Omega(x, t)); declare(U(xi)); declare(V(xi)); declare(G(xi))

Omega(x, t)*`will now be displayed as`*Omega

  

U(xi)*`will now be displayed as`*U

  

V(xi)*`will now be displayed as`*V

  

G(xi)*`will now be displayed as`*G

 (2)
> 

ode := 4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

4*V(xi)^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*V(xi)^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*V(xi)^2-2*V(xi)*(diff(diff(V(xi), xi), xi))*alpha*m*n+(-alpha*m^2+2*alpha*m*n)*(diff(V(xi), xi))^2 = 0

 (3)
> 

S := (diff(G(xi), xi))^2 = a*G(xi)^2+b*G(xi)^3+c*G(xi)^4

(diff(G(xi), xi))^2 = a*G(xi)^2+b*G(xi)^3+c*G(xi)^4

 (4)
> 

S1 := sum(A[i]*G(xi)^i, i = 0 .. 1)

A[0]+A[1]*G(xi)

 (5)
> 

S12 := diff(S1, xi)

A[1]*(diff(G(xi), xi))

 (6)
> 

S123 := diff(G(xi), xi) = sqrt(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)

diff(G(xi), xi) = (a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (7)
> 

subs(S123, S12)

A[1]*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (8)
> 

S11 := %

A[1]*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (9)
> 

S2 := diff(S11, xi)

(1/2)*A[1]*(2*a*G(xi)*(diff(G(xi), xi))+3*b*G(xi)^2*(diff(G(xi), xi))+4*c*G(xi)^3*(diff(G(xi), xi)))/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (10)
> 

S22 := subs(S123, S2)

(1/2)*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (11)
> 

K := V(xi) = S1

V(xi) = A[0]+A[1]*G(xi)

 (12)
> 

K1 := diff(V(xi), xi) = S11

diff(V(xi), xi) = A[1]*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (13)
> 

K2 := diff(V(xi), xi, xi) = S22

diff(diff(V(xi), xi), xi) = (1/2)*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (14)
> 

F := eval(ode, {K, K1, K2})

4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0

 (15)
> 

numer(lhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0))*denom(rhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0)) = numer(rhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0))*denom(lhs(4*(A[0]+A[1]*G(xi))^4*n^2*sigma+(-4*beta*k*m*n^2+4*gamma*k*m*n^2)*(A[0]+A[1]*G(xi))^3+(4*alpha*k^2*m^2*n^2-4*delta^2*m*n^2+4*m*n^2*w)*(A[0]+A[1]*G(xi))^2-(A[0]+A[1]*G(xi))*A[1]*(2*a*G(xi)*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+3*b*G(xi)^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+4*c*G(xi)^3*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2))*alpha*m*n/(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)+(-alpha*m^2+2*alpha*m*n)*A[1]^2*(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4) = 0))

-(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)*(4*delta^2*m*n^2*A[0]^2-4*m*n^2*w*A[0]^2-4*G(xi)^4*n^2*sigma*A[1]^4-8*G(xi)*alpha*k^2*m^2*n^2*A[0]*A[1]+4*G(xi)^3*alpha*c*m*n*A[0]*A[1]-12*G(xi)*gamma*k*m*n^2*A[0]^2*A[1]+12*G(xi)*beta*k*m*n^2*A[0]^2*A[1]+3*G(xi)^2*alpha*b*m*n*A[0]*A[1]+2*G(xi)*a*alpha*m*n*A[0]*A[1]-12*G(xi)^2*gamma*k*m*n^2*A[0]*A[1]^2+12*G(xi)^2*beta*k*m*n^2*A[0]*A[1]^2-4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3+G(xi)^4*alpha*c*m^2*A[1]^2-16*G(xi)^3*n^2*sigma*A[0]*A[1]^3+G(xi)^3*alpha*b*m^2*A[1]^2+4*G(xi)^2*delta^2*m*n^2*A[1]^2-24*G(xi)^2*n^2*sigma*A[0]^2*A[1]^2+G(xi)^2*a*alpha*m^2*A[1]^2-4*G(xi)^2*m*n^2*w*A[1]^2-16*G(xi)*n^2*sigma*A[0]^3*A[1]-4*gamma*k*m*n^2*A[0]^3-4*n^2*sigma*A[0]^4-4*G(xi)^3*gamma*k*m*n^2*A[1]^3+4*G(xi)^3*beta*k*m*n^2*A[1]^3-4*G(xi)^2*alpha*k^2*m^2*n^2*A[1]^2+2*G(xi)^4*alpha*c*m*n*A[1]^2+G(xi)^3*alpha*b*m*n*A[1]^2+8*G(xi)*delta^2*m*n^2*A[0]*A[1]-8*G(xi)*m*n^2*w*A[0]*A[1]) = 0

 (16)
> 

%/(-sqrt(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4))

4*delta^2*m*n^2*A[0]^2-4*m*n^2*w*A[0]^2-4*G(xi)^4*n^2*sigma*A[1]^4-8*G(xi)*alpha*k^2*m^2*n^2*A[0]*A[1]+4*G(xi)^3*alpha*c*m*n*A[0]*A[1]-12*G(xi)*gamma*k*m*n^2*A[0]^2*A[1]+12*G(xi)*beta*k*m*n^2*A[0]^2*A[1]+3*G(xi)^2*alpha*b*m*n*A[0]*A[1]+2*G(xi)*a*alpha*m*n*A[0]*A[1]-12*G(xi)^2*gamma*k*m*n^2*A[0]*A[1]^2+12*G(xi)^2*beta*k*m*n^2*A[0]*A[1]^2-4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3+G(xi)^4*alpha*c*m^2*A[1]^2-16*G(xi)^3*n^2*sigma*A[0]*A[1]^3+G(xi)^3*alpha*b*m^2*A[1]^2+4*G(xi)^2*delta^2*m*n^2*A[1]^2-24*G(xi)^2*n^2*sigma*A[0]^2*A[1]^2+G(xi)^2*a*alpha*m^2*A[1]^2-4*G(xi)^2*m*n^2*w*A[1]^2-16*G(xi)*n^2*sigma*A[0]^3*A[1]-4*gamma*k*m*n^2*A[0]^3-4*n^2*sigma*A[0]^4-4*G(xi)^3*gamma*k*m*n^2*A[1]^3+4*G(xi)^3*beta*k*m*n^2*A[1]^3-4*G(xi)^2*alpha*k^2*m^2*n^2*A[1]^2+2*G(xi)^4*alpha*c*m*n*A[1]^2+G(xi)^3*alpha*b*m*n*A[1]^2+8*G(xi)*delta^2*m*n^2*A[0]*A[1]-8*G(xi)*m*n^2*w*A[0]*A[1] = 0

 (17)
> 

collect(%, G)

(-4*n^2*sigma*A[1]^4+alpha*c*m^2*A[1]^2+2*alpha*c*m*n*A[1]^2)*G(xi)^4+(4*beta*k*m*n^2*A[1]^3-4*gamma*k*m*n^2*A[1]^3-16*n^2*sigma*A[0]*A[1]^3+alpha*b*m^2*A[1]^2+alpha*b*m*n*A[1]^2+4*alpha*c*m*n*A[0]*A[1])*G(xi)^3+(-4*alpha*k^2*m^2*n^2*A[1]^2+12*beta*k*m*n^2*A[0]*A[1]^2-12*gamma*k*m*n^2*A[0]*A[1]^2+4*delta^2*m*n^2*A[1]^2-24*n^2*sigma*A[0]^2*A[1]^2+a*alpha*m^2*A[1]^2+3*alpha*b*m*n*A[0]*A[1]-4*m*n^2*w*A[1]^2)*G(xi)^2+(-8*alpha*k^2*m^2*n^2*A[0]*A[1]+12*beta*k*m*n^2*A[0]^2*A[1]-12*gamma*k*m*n^2*A[0]^2*A[1]+8*delta^2*m*n^2*A[0]*A[1]-16*n^2*sigma*A[0]^3*A[1]+2*a*alpha*m*n*A[0]*A[1]-8*m*n^2*w*A[0]*A[1])*G(xi)-4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3-4*gamma*k*m*n^2*A[0]^3+4*delta^2*m*n^2*A[0]^2-4*n^2*sigma*A[0]^4-4*m*n^2*w*A[0]^2 = 0

 (18)
> 

eq0 := -4*alpha*k^2*m^2*n^2*A[0]^2+4*beta*k*m*n^2*A[0]^3-4*gamma*k*m*n^2*A[0]^3+4*delta^2*m*n^2*A[0]^2-4*n^2*sigma*A[0]^4-4*m*n^2*w*A[0]^2 = 0
> 

eq1 := -8*alpha*k^2*m^2*n^2*A[0]*A[1]+12*beta*k*m*n^2*A[0]^2*A[1]-12*gamma*k*m*n^2*A[0]^2*A[1]+8*delta^2*m*n^2*A[0]*A[1]-16*n^2*sigma*A[0]^3*A[1]+2*a*alpha*m*n*A[0]*A[1]-8*m*n^2*w*A[0]*A[1] = 0
> 

eq2 := -4*alpha*k^2*m^2*n^2*A[1]^2+12*beta*k*m*n^2*A[0]*A[1]^2-12*gamma*k*m*n^2*A[0]*A[1]^2+4*delta^2*m*n^2*A[1]^2-24*n^2*sigma*A[0]^2*A[1]^2+a*alpha*m^2*A[1]^2+3*alpha*b*m*n*A[0]*A[1]-4*m*n^2*w*A[1]^2 = 0
> 

eq3 := 4*beta*k*m*n^2*A[1]^3-4*gamma*k*m*n^2*A[1]^3-16*n^2*sigma*A[0]*A[1]^3+alpha*b*m^2*A[1]^2+alpha*b*m*n*A[1]^2+4*alpha*c*m*n*A[0]*A[1] = 0
> 

eq4 := -4*n^2*sigma*A[1]^4+alpha*c*m^2*A[1]^2+2*alpha*c*m*n*A[1]^2 = 0
> 

C := solve({eq0, eq1, eq2, eq3, eq4}, {a, b, c, A[0]})

{a = 4*n^2*(alpha*k^2*m-delta^2+w)/(m*alpha), b = 4*(gamma-beta)*k*n^2*A[1]/((m+n)*alpha), c = 4*n^2*sigma*A[1]^2/(alpha*m*(m+2*n)), A[0] = 0}

 (19)
> 

W := q(x, t) = V(xi)^(1/(2*n))

q(x, t) = V(xi)^((1/2)/n)

 (20)
> 

S123 := diff(G(xi), xi) = sqrt(a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)

diff(G(xi), xi) = (a*G(xi)^2+b*G(xi)^3+c*G(xi)^4)^(1/2)

 (21)
> 

dsolve(S, G(xi))

G(xi) = (1/2)*(-b+(-4*a*c+b^2)^(1/2))/c, G(xi) = -(1/2)*(b+(-4*a*c+b^2)^(1/2))/c, G(xi) = -4*a*exp(c__1*a^(1/2))/(exp(xi*a^(1/2))*(4*a*c-b^2+2*exp(c__1*a^(1/2))*b/exp(xi*a^(1/2))-(exp(c__1*a^(1/2)))^2/(exp(xi*a^(1/2)))^2)), G(xi) = -4*a*exp(xi*a^(1/2))/(exp(c__1*a^(1/2))*(4*a*c-b^2+2*exp(xi*a^(1/2))*b/exp(c__1*a^(1/2))-(exp(xi*a^(1/2)))^2/(exp(c__1*a^(1/2)))^2))

 (22)

Download AUX-M.mw

is nonsense iam stuck for something like that

reply...

salim-barzani 1560
December 24 2024
0 0

@nm  can we have same solution becuase he use case in that paper i need to get the same solution becuase there is function which i must figure out the same solution and i am stuck at this point how he get this two solution, How by assuming he get thus solution i try to use mathematica  but all my code are maple  and i can't get it in there too, and also someone in mathematica check that the solution of paper is not solution and is not satisfy equation 

How i can get the same at lease get the same as mathmatica 

no one response and no one know about hi...

salim-barzani 1560
December 24 2024
0 0

@acer and becuase moderator  delete my questions even when is not the same  i will delete all

reply...

salim-barzani 1560
December 24 2024
0 0

@janhardo  watch equation 14 have two solution becuase ODE have degree two is like quadratic equation when have two root

yea i did all because......

salim-barzani 1560
December 24 2024
0 0

@acer  i delete it , in case i undrestand more about hirota and post with more detail  i work on it and i don't know when i finish the work but my target is still remain  about finding best way for finding D-operator  of any NPDE. and indeed when i post a different one two just becuase contain hirota moderator delete my post becuase of that i did.
why there is any problem?

you are so good...

salim-barzani 1560
December 23 2024
0 0

@acer  I have a habit that unless I see something, I can’t do it. What you’re saying is very easy, but I haven’t seen it.

we don't know this stuff !...

salim-barzani 1560
December 23 2024
0 0

@acer each time we get this problem we post here fixed for us , i watch your code and me is not have any different but your code run mine not . my maple don't have 1D it work for latex too so

what is different?...

salim-barzani 1560
December 23 2024
0 0

@acer i can't see any different?

just one more question...

salim-barzani 1560
December 21 2024
0 0

@acer i just ask one more question a new algorithm i find know with a lot of example included ,i have to post this one 

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