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salim-barzani

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1 years, 16 days
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salim-barzani 1555
April 20 2025
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@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 1555
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 1555
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 1555
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 1555
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 1555
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 1555
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?

explaning this topic is hard a little bi...

salim-barzani 1555
April 16 2025
0 0

@Carl Love this is not about result this is have another trick which i can't see , as you saw the paper how they did that? in all paper they did this but why i can't reach the result? i have a series for get eq(16) but is not applying long wave limit,  so they did something which we can't figure out,  i have to figure out , maybe someone did that before and someone intrested like me , i hope  find  this 

i will ask another question which is rel...

salim-barzani 1555
April 16 2025
0 0

@dharr 
I honestly think the problem itself is not too difficult, but the method for finding the solution is quite challenging. We don’t see it the same way the authors do. In many papers, they plot this line directly, but for me, it’s a big challenge, I can't even figure out how they’re getting it.

I need to finish this work, but this approach to solving the problem is causing me a lot of difficulty. In my next question, you’ll see that they use a different method, if I can understand how to apply that limit and use it to find the line, it could help me a lot. Right now, I'm working on figuring out how to determine this line for all the cases. It seems to be related to velocity in some way.

Please, your help on my next question would mean a lot to me.

reply...

salim-barzani 1555
April 16 2025

@janhardo  my deepseek is like that i can't work with it!

 

about  Bäcklund transformations, Lax pairs i didn't work with them now, but there is more simple work with bilinear form we don't need package even i can get any bilinear form without using this, but for finding auxiliary i have problem  for my last equation when auxiliary is u=u0+ln(f)_x  try this method maybe you can generate a series 

https://www.mapleprimes.com/questions/239878-How-Collect-A-Fraction-Which-Contain
try use this series i am sure they use this to find that kind of auxiliary 

I didn't save last file?...

salim-barzani 1555
April 16 2025
0 0

I didn't save last file , nonsense they do dublicate most of questions 

Send me mail please...

salim-barzani 1555
April 16 2025

@janhardo i will explain more on  mail send me one please, have another trick which you don't know and maybe you can find general one with this special Ai you have 

So you can find for all? by this formul...

salim-barzani 1555
April 16 2025

@janhardo i like this topic and really is important to me you can find for all by this method ? also if this method is good so you have tt construct for (1+1)D and (2+1)D and (3+1)D also if possible for (4+1) additionally this is the  impotant part of solving some of equation i have  really they  hard  auxiliary which i can't find it , for example this kind i didn't found them even one of them untill now, and please upload the file 

 

They said same thing as you, but I didn'...

salim-barzani 1555
April 15 2025
0 0

@dharr they say maple can't do that but i told them there is nothing which maple can't but I accepted know by your comment thank you dear Dr.david

i don't have info about that , but ......

salim-barzani 1555
April 15 2025
0 0

@mmcdara  after i finish my work about soliton then i will come to this kind of fluid and i will try use maple for sure, i am sure maple can do that work  too, ofcurse you and Dr.david and moderator and so on are best helper in here 

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