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salim-barzani

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1 years, 34 days
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this is true , but how, can you apply fo...

salim-barzani 1565
April 20 2025
0 0

@janhardo this true but How reach this is so perfect you get F[3] can you test for N=2 and N=4 N=5 we have that and if it is true then it is done!

this so diferent from what i want!!!...

salim-barzani 1565
April 20 2025
0 0

@janhardo i don't want N-soliton i want apply long wave limit  with tylor series to N-soliton solution to get that function  F[3] function F[3] is example but apply first for N=2 is more esier the F[2]=theta[1]*theta[2]+B[12] if we get this then we can do for N=3,4,5,6,...

so far...

salim-barzani 1565
April 20 2025
0 0

@janhardo  if N=3 we have to get this 

You are so near to find...

salim-barzani 1565
April 20 2025
0 0

@janhardo in F[3] i mention in picture in top have exponential we have to apply long wave limit just for k1-k2-->0 and other remain so how we do that?

I can't work with thus code...

salim-barzani 1565
April 20 2025
0 0

@janhardo  no thus code are useless i have my own code but they are so complicated and have a lot of part because of that I can't upload here , i know all part to change it  but i don't know where is mistak , if you give my code to your ai maybe ai can finish the work

wrong !...

salim-barzani 1565
April 20 2025
0 0

@janhardo  he use that function i give it in picture, i want acheive them by that substitution i mentioned and apply   long wave limit and   apply series so How we can reach this the F_2 is easiest one if you can reach F_2  when N-2 we have F_2=theta[1]*theta[2]+B[1,2] if you find this you will find other first try find this then you can reach other too also i mentioned a file of series in top why didn't use that series i will upload here too 

N-S.mw

reply...

salim-barzani 1565
April 20 2025
0 0

@janhardo  this is some of that function when k[1]-k[2]-->0 

 

This is what i am talking about !!!! but...

salim-barzani 1565
April 20 2025
0 0

@janhardo  i have in paper i have function untill F_5 after applying long wave limit  can you do that ? this is great answer he did this is exactly we want

reply...

salim-barzani 1565
April 20 2025
0 0

@janhardo is not about ploting , i can plot 1000 lump togehter like that , i want to know how the series change to  lump series becuase we have interaction betwen them if don't know how get this series by applying (long wave limit) we can't do that interaction too,  i have other paper solved too but i will mention this, from my question in top , i uploaded all structure eq(6) is the series i uploaded for you we have that series by changing the transformation apply  eq(15) to series eq(6) we have to get eq(16), don't look for solution or graph just how this transformation happen by applying long wave limit? i will upload some picture in other paper too

 

 

i try like this but i didn't get answer open the mw file


 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

  
> 

``
> 

declare(u(x, y, z, t))

u(x, y, z, t)*`will now be displayed as`*u

 (1)
> 

declare(f(x, y, z, t))

f(x, y, z, t)*`will now be displayed as`*f

 (2)
> 

alpha := 1; beta := 1; delta := 1; lambda := 1

1

  

1

  

1

  

1

 (3)
> 

pde := diff(diff(u(x, y, z, t), t)+6*u(x, y, z, t)*(diff(u(x, y, z, t), x))+diff(u(x, y, z, t), `$`(x, 3)), x)-lambda*(diff(u(x, y, z, t), `$`(y, 2)))+diff(alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+delta*(diff(u(x, y, z, t), z)), x)

diff(diff(u(x, y, z, t), t), x)+6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)-(diff(diff(u(x, y, z, t), y), y))+diff(diff(u(x, y, z, t), x), x)+diff(diff(u(x, y, z, t), x), y)+diff(diff(u(x, y, z, t), x), z)

 (4)
> 

thetai := t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]
> 

eq15 := w[i] = -(k[i]^4+k[i]^2+k[i]*l[i]+k[i]*r[i]-l[i]^2)/k[i]
> 

eq17 := u(x, y, z, t) = 2*(diff(diff(f(x, y, z, t), x), x))/f(x, y, z, t)-2*(diff(f(x, y, z, t), x))^2/f(x, y, z, t)^2
> 

A[sj] := (3*k[i]^4*k[j]^2-6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)/(3*k[i]^4*k[j]^2+6*k[i]^3*k[j]^3+(3*k[j]^4+l[j]^2)*k[i]^2-2*k[i]*k[j]*l[i]*l[j]+k[j]^2*l[i]^2)
> 

F2 := 1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])

1+exp(eta[1])+b[1, 2]*exp(eta[1]+eta[2])+exp(eta[2])

 (5)
> 

F22 := 1+exp(eta[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(eta[1]+eta[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(eta[2])

1+exp(eta[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(eta[1]+eta[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(eta[2])

 (6)
> 

NULL
> 

NULL
> 

F222 := exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])

exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1])+(3*k[1]^4*k[2]^2-6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)*exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])/(3*k[1]^4*k[2]^2+6*k[1]^3*k[2]^3+(3*k[2]^4+l[2]^2)*k[1]^2-2*k[1]*k[2]*l[1]*l[2]+k[2]^2*l[1]^2)+exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])

 (7)
> 

indets(F222)

{t, x, y, eta[1], eta[2], k[1], k[2], l[1], l[2], r[1], r[2], exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]), exp(-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2]), exp(-(t*k[1]^4+t*k[1]^2+t*k[1]*l[1]+t*k[1]*r[1]-t*l[1]^2-x*k[1]^2-y*k[1]*l[1]-eta[1]*k[1])/k[1]-(t*k[2]^4+t*k[2]^2+t*k[2]*l[2]+t*k[2]*r[2]-t*l[2]^2-x*k[2]^2-y*k[2]*l[2]-eta[2]*k[2])/k[2])}

 (8)
> 

eq1 := eval(F222, {k[1] = K[1]*epsilon, k[2] = K[2]*epsilon, l[1] = L[1]*epsilon, l[2] = L[2]*epsilon, r[1] = R[1]*epsilon, r[2] = R[2]*epsilon, exp(eta[1]) = -1, exp(eta[2]) = -1})

exp(-(epsilon^4*t*K[1]^4+epsilon^2*t*K[1]^2+epsilon^2*t*K[1]*L[1]+epsilon^2*t*K[1]*R[1]-epsilon^2*t*L[1]^2-epsilon^2*x*K[1]^2-epsilon^2*y*K[1]*L[1]-epsilon*K[1]*eta[1])/(K[1]*epsilon))+(3*K[1]^4*epsilon^6*K[2]^2-6*K[1]^3*epsilon^6*K[2]^3+(3*epsilon^4*K[2]^4+epsilon^2*L[2]^2)*K[1]^2*epsilon^2-2*K[1]*epsilon^4*K[2]*L[1]*L[2]+K[2]^2*epsilon^4*L[1]^2)*exp(-(epsilon^4*t*K[1]^4+epsilon^2*t*K[1]^2+epsilon^2*t*K[1]*L[1]+epsilon^2*t*K[1]*R[1]-epsilon^2*t*L[1]^2-epsilon^2*x*K[1]^2-epsilon^2*y*K[1]*L[1]-epsilon*K[1]*eta[1])/(K[1]*epsilon)-(epsilon^4*t*K[2]^4+epsilon^2*t*K[2]^2+epsilon^2*t*K[2]*L[2]+epsilon^2*t*K[2]*R[2]-epsilon^2*t*L[2]^2-epsilon^2*x*K[2]^2-epsilon^2*y*K[2]*L[2]-epsilon*K[2]*eta[2])/(K[2]*epsilon))/(3*K[1]^4*epsilon^6*K[2]^2+6*K[1]^3*epsilon^6*K[2]^3+(3*epsilon^4*K[2]^4+epsilon^2*L[2]^2)*K[1]^2*epsilon^2-2*K[1]*epsilon^4*K[2]*L[1]*L[2]+K[2]^2*epsilon^4*L[1]^2)+exp(-(epsilon^4*t*K[2]^4+epsilon^2*t*K[2]^2+epsilon^2*t*K[2]*L[2]+epsilon^2*t*K[2]*R[2]-epsilon^2*t*L[2]^2-epsilon^2*x*K[2]^2-epsilon^2*y*K[2]*L[2]-epsilon*K[2]*eta[2])/(K[2]*epsilon))

 (9)
> 

G := limit(eq1, epsilon = 0)

exp(eta[1])+exp(eta[2])+exp(eta[1]+eta[2])

 (10)
> 

NULL
> 

NULL
> 

NULL
> 

NULL
> 

NULL

NULL


 

Download LWL.mw

reply...

salim-barzani 1565
April 20 2025
0 0

@janhardo  we need change series equation (6) to equation 16 by applying the transformation equation (15)  if we do that i will do the rest, becuase there is a lot kind of other interaction which  we need to apply long wave  limit method to series equation(6)  this is sereis equation (6) when N=2

N-S.mw

we have to change this series to equation(16) by apply that transformation

many thanks john......

salim-barzani 1565
April 19 2025
0 0

@janhardo  i did it, thank to your Ai i know now how to solve, can you tell me about this Ai you use it is deepseek ? in my pc not working but in my ipad work i didn't work with Ai but if i know it is work really i will try ?

can you use your Ai for this question too https://www.mapleprimes.com/questions/240218-How-Apply-Substitution-And-Apply-Limit

really it is more than 2 month i am working on it and i don't know how apply long wave limit for N-soliton series that series you found it last time?

reply...

salim-barzani 1565
April 19 2025
0 0

@janhardo i need find l[2] and after substitute in u(x,y,z,t) must satisfy the pdetest, first answer of yours is true but how find that r[2] ? just try upload that file for me please if you know?

How you did that?...

salim-barzani 1565
April 19 2025
0 0

@janhardo upload file if you have it,  i want to find the parameter? the paper didn't mention anything about f where to put it and then solve the equation for finding parameter

Can you work on this question?...

salim-barzani 1565
April 17 2025

@janhardo  Can you use your ai for getting the results is a lot of time I can't get it maybe you can 

https://www.mapleprimes.com/questions/240218-How-Apply-Substitution-And-Apply-Limit

🇮🇶 iraq , it work on ipad but i want i...

salim-barzani 1565
April 17 2025

@janhardo use the series when the series is u=a*ln(f)_xx+b*ln(f)_x+c find parameter a,b,c after substituting in our pde in most equation b and c are zero but in some of them c is not zero , i told you send me email for give you a note about bilinear form why not sended?

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