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How find Auxiliary solution function by using seri...

Asked by: salim-barzani 1555
substitution pde series
March 26 2025
4  0

in a lot of paper i see that they just use the Auxiliary function without mention any detail but now i have to find out how i can reach this function, always i used u=Rdiff(ln(f),x#1,2) or u=Rdiff(ln(f),y,x)  (eq17) in mw. and it is answer for me untill now without knowing finding, but i have to figure out how they reach this in more than 1000 paper i didn't see any explanation about that they just used just in one of the paper mentioned something  like a series which i think they used this series but again is so complicated for undrestanding , i will put some problem picture and now i want to know how find them  eq17 for any equation based on the series in last picture mentioned

 

second example

third example which is so  different from other and i don't know how author reach this point 

i have to find this auxiliary function by using something like series  as mentioned in other question? how i can use this series for finding my auxiliary function u= u_0+R*diff(ln(f),x)  


 

#picture one

NULL

> 

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.

  
> 

undeclare(prime)

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

 (1)
> 

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

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

 (2)
> 

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

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

 (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), `$`(x, 3)), x)+diff(alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+delta*(diff(u(x, y, z, t), z)), x)+mu*(diff(u(x, y, z, t), `$`(t, 2)))

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)+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))+mu*(diff(diff(u(x, y, z, t), t), t))

 (4)
> 

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, z, t) = a*u(x, y, z, t)))/a, a) end proc, expand(pde))

diff(diff(u(x, y, z, t), t), x)+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+delta*(diff(diff(u(x, y, z, t), x), z))+mu*(diff(diff(u(x, y, z, t), t), t)), 6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))

 (5)
> 

thetai := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]; eval(pde_linear, u(x, y, z, t) = exp(thetai)); eq15 := isolate(%, w[i])

k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

  

k[i]^2*w[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+k[i]^4*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+alpha*k[i]^2*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+beta*k[i]^2*l[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+delta*k[i]^2*r[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+mu*k[i]^2*w[i]^2*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])

  

w[i] = (1/2)*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu

 (6)
> 

eqf := f(x, y, z, t) = 1+eval(exp(thetai), eq15)

f(x, y, z, t) = 1+exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i])

 (7)
> 

eq17 := u(x, y, z, t) = R*(diff(ln(f(x, y, z, t)), `$`(x, 2)))

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

 (8)
> 

eval(eq17, eqf); simplify(eval(pde, %)); sort([solve(%, R)]); eq17 := eval(eq17, R = simplify(%[2]))

u(x, y, z, t) = R*(k[i]^2*exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i])/(1+exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i]))-k[i]^2*(exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i]))^2/(1+exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i]))^2)

  

12*R*k[i]^6*exp(((1+(-4*beta*l[i]-4*delta*r[i]-4*k[i]^2-4*alpha)*mu)^(1/2)*t*k[i]+((2*y*l[i]+2*z*r[i]+2*x)*mu-t)*k[i]+2*eta[i]*mu)/mu)*(exp(((1+(-4*beta*l[i]-4*delta*r[i]-4*k[i]^2-4*alpha)*mu)^(1/2)*t*k[i]+((2*y*l[i]+2*z*r[i]+2*x)*mu-t)*k[i]+2*eta[i]*mu)/mu)-3*exp((1/2)*((1+(-4*beta*l[i]-4*delta*r[i]-4*k[i]^2-4*alpha)*mu)^(1/2)*t*k[i]+((2*y*l[i]+2*z*r[i]+2*x)*mu-t)*k[i]+2*eta[i]*mu)/mu)+1)*(R-2)/(1+exp((1/2)*((1+(-4*beta*l[i]-4*delta*r[i]-4*k[i]^2-4*alpha)*mu)^(1/2)*t*k[i]+((2*y*l[i]+2*z*r[i]+2*x)*mu-t)*k[i]+2*eta[i]*mu)/mu))^6

  

[0, 2]

  

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

 (9)
> 

eq19 := eval(eq17, eqf)

u(x, y, z, t) = 2*k[i]^2*exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i])/(1+exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i]))-2*k[i]^2*(exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i]))^2/(1+exp(k[i]*((1/2)*t*(-1+(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1)^(1/2))/mu+y*l[i]+z*r[i]+x)+eta[i]))^2

 (10)
> 

simplify(eq19)

u(x, y, z, t) = 2*k[i]^2*exp((1/2)*((1+(-4*beta*l[i]-4*delta*r[i]-4*k[i]^2-4*alpha)*mu)^(1/2)*t*k[i]+((2*y*l[i]+2*z*r[i]+2*x)*mu-t)*k[i]+2*eta[i]*mu)/mu)/(1+exp((1/2)*((1+(-4*beta*l[i]-4*delta*r[i]-4*k[i]^2-4*alpha)*mu)^(1/2)*t*k[i]+((2*y*l[i]+2*z*r[i]+2*x)*mu-t)*k[i]+2*eta[i]*mu)/mu))^2

 (11)
> 

pdetest(eq19, pde)

0

 (12)
> 

#second example
> 

NULL
> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)
> 

``

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

 (13)
> 

declare(u(x, y, t))

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

 (14)
> 

declare(f(x, y, t))

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

 (15)
> 

pde := diff(u(x, y, t), x, t)+alpha*(diff(u(x, y, t), `$`(x, 4))+6*(diff(u(x, y, t), x))*(diff(u(x, y, t), `$`(x, 2))))+beta*(diff(u(x, y, t), `$`(y, 2)))+a*(diff(u(x, y, t), `$`(x, 2)))+b*(diff(u(x, y, t), x, y))

diff(diff(u(x, y, t), t), x)+alpha*(diff(diff(diff(diff(u(x, y, t), x), x), x), x)+6*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), x)))+beta*(diff(diff(u(x, y, t), y), y))+a*(diff(diff(u(x, y, t), x), x))+b*(diff(diff(u(x, y, t), x), y))

 (16)
> 

oppde := [op(expand(pde))]; u_occurrences := map(proc (i) options operator, arrow; numelems(select(has, [op([op(i)])], u)) end proc, oppde); linear_op_indices := ListTools:-SearchAll(1, u_occurrences); pde_linear := add(oppde[[linear_op_indices]]); pde_nonlinear := expand(simplify(expand(pde)-pde_linear))

diff(diff(u(x, y, t), t), x)+alpha*(diff(diff(diff(diff(u(x, y, t), x), x), x), x))+beta*(diff(diff(u(x, y, t), y), y))+a*(diff(diff(u(x, y, t), x), x))+b*(diff(diff(u(x, y, t), x), y))

  

6*alpha*(diff(u(x, y, t), x))*(diff(diff(u(x, y, t), x), x))

 (17)
> 

thetai := k[i]*(t*w[i]+y*l[i]+x)+eta[i]; eval(pde_linear, u(x, y, t) = 1+exp(thetai)); eq15 := isolate(%, w[i])

k[i]*(t*w[i]+y*l[i]+x)+eta[i]

  

k[i]^2*w[i]*exp(k[i]*(t*w[i]+y*l[i]+x)+eta[i])+alpha*k[i]^4*exp(k[i]*(t*w[i]+y*l[i]+x)+eta[i])+beta*k[i]^2*l[i]^2*exp(k[i]*(t*w[i]+y*l[i]+x)+eta[i])+a*k[i]^2*exp(k[i]*(t*w[i]+y*l[i]+x)+eta[i])+b*k[i]^2*l[i]*exp(k[i]*(t*w[i]+y*l[i]+x)+eta[i])

  

w[i] = -alpha*k[i]^2-beta*l[i]^2-b*l[i]-a

 (18)
> 

eqf := f(x, y, t) = 1+eval(exp(thetai), eq15)

f(x, y, t) = 1+exp(k[i]*((-alpha*k[i]^2-beta*l[i]^2-b*l[i]-a)*t+l[i]*y+x)+eta[i])

 (19)
> 

eq17 := u(x, y, t) = R*(diff(ln(f(x, y, t)), x))

u(x, y, t) = R*(diff(f(x, y, t), x))/f(x, y, t)

 (20)
> 

eval(eq17, eqf); simplify(eval(pde, %)); sort([solve(%, R)]); eq17 := eval(eq17, R = simplify(%[2]))

[0, 2]

  

u(x, y, t) = 2*(diff(f(x, y, t), x))/f(x, y, t)

 (21)
> 

eq19 := eval(eq17, eqf)

u(x, y, t) = 2*k[i]*exp(k[i]*((-alpha*k[i]^2-beta*l[i]^2-b*l[i]-a)*t+l[i]*y+x)+eta[i])/(1+exp(k[i]*((-alpha*k[i]^2-beta*l[i]^2-b*l[i]-a)*t+l[i]*y+x)+eta[i]))

 (22)
> 

M := eval(rhs(eq19), i = 1)

2*k[1]*exp(k[1]*(t*(-alpha*k[1]^2-beta*l[1]^2-b*l[1]-a)+y*l[1]+x)+eta[1])/(1+exp(k[1]*(t*(-alpha*k[1]^2-beta*l[1]^2-b*l[1]-a)+y*l[1]+x)+eta[1]))

 (23)
> 

simplify(eq19)

u(x, y, t) = 2*k[i]*exp(-alpha*t*k[i]^3+((-beta*l[i]^2-b*l[i]-a)*t+y*l[i]+x)*k[i]+eta[i])/(1+exp(-alpha*t*k[i]^3+((-beta*l[i]^2-b*l[i]-a)*t+y*l[i]+x)*k[i]+eta[i]))

 (24)
> 

pdetest(eq19, pde)

0

 (25)
> 

#third example which is so different and really i don't know how the author reach this point? which is diff(arctan(f),x)?
> 

NULL
> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

_local(gamma)
> 

undeclare(prime)

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

 (26)
> 

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

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

 (27)
> 

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

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

 (28)
> 

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

diff(u(x, y, z, t), t)+6*u(x, y, z, t)^2*(diff(u(x, y, z, t), x))+diff(diff(diff(u(x, y, z, t), x), x), x)+alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+delta*(diff(u(x, y, z, t), z))+lambda*(diff(diff(u(x, y, z, t), t), x))+mu*(diff(diff(u(x, y, z, t), t), t))

 (29)
> 

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, z, t) = a*u(x, y, z, t)))/a, a) end proc, expand(pde))

diff(u(x, y, z, t), t)+diff(diff(diff(u(x, y, z, t), x), x), x)+alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+delta*(diff(u(x, y, z, t), z))+lambda*(diff(diff(u(x, y, z, t), t), x))+mu*(diff(diff(u(x, y, z, t), t), t)), 6*u(x, y, z, t)^2*(diff(u(x, y, z, t), x))

 (30)
> 

thetai := k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]; eval(pde_linear, u(x, y, z, t) = exp(thetai)); eq15 := isolate(%, w[i])

k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i]

  

k[i]*w[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+k[i]^3*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+alpha*k[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+beta*k[i]*l[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+delta*k[i]*r[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+lambda*k[i]^2*w[i]*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])+mu*k[i]^2*w[i]^2*exp(k[i]*(t*w[i]+y*l[i]+z*r[i]+x)+eta[i])

  

w[i] = (1/2)*(-lambda*k[i]-1+(-4*beta*mu*k[i]*l[i]-4*delta*mu*k[i]*r[i]+lambda^2*k[i]^2-4*mu*k[i]^3-4*alpha*mu*k[i]+2*lambda*k[i]+1)^(1/2))/(mu*k[i])

 (31)
> 

eqf := f(x, y, z, t) = 1+eval(exp(thetai), eq15)

f(x, y, z, t) = 1+exp(k[i]*((1/2)*(-lambda*k[i]-1+(-4*beta*mu*k[i]*l[i]-4*delta*mu*k[i]*r[i]+lambda^2*k[i]^2-4*mu*k[i]^3-4*alpha*mu*k[i]+2*lambda*k[i]+1)^(1/2))*t/(mu*k[i])+l[i]*y+r[i]*z+x)+eta[i])

 (32)
> 

eq17 := u(x, y, z, t) = R*(diff(ln(f(x, y, z, t)), x))

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

 (33)
> 

eval(eq17, eqf); simplify(eval(pde, %)); sort([solve(%, R)]); eq17 := eval(eq17, R = simplify(%[2]))


 

Download F-series.mw

Thanks for any help!

Maple Online Help...

Asked by: Henning Broge 10
documentation online
March 26 2025
2  0

Hi

does anyone know when Maple Online Help will be up again?

Regards

Henning

Does Maple 2025 have a dark theme yet?...

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Does Maple 2025 have a dark theme or GUI color customization?

How to resize Maple 2025 to half of the screen...

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March 25 2025
2  8

Neither dragging the Maple Window to the screen edge nor Windows key & Arrow keys works on my
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Is this only my installation?

Anything I can do get normal Windows windows behaviour back?

Maple 2025 - TextArea component ignores zoom facto...

Asked by: Anthrazit 885
March 25 2025
1  0

I've posted this issue in the beta forum for Maple previously, but apparently this issue was never addressed, so I am going to repost it here.

Contrary to Maple 2024, components like TextArea now ignore the general view zoom factor in Maple 2025.

I'll submit it as a software change request once Maple 2025 is on the list.

Converting math to text but still executing...

Asked by: PerKirkegaard64 20
March 25 2025
0  2

I have a student who has a problem when closing and opening a Maple file.

It seems as if Maple turns math fields into text, but still execute when using ! or !!!

The dark red part is written in a text field, but Maple still executes

If I try to write in a math field and executes, closes Maple and opens again, this does not happen, so it is not the file that is the problem.  The student is running 2024.2 version.

Can anyone explain the problem and how to solve it.

 

I am unable to add a comment or the file. I have tried several times, without any luck

How to find a subscript in 2-D Math...

Asked by: C_R 3412
2dmath subscript search
March 22 2025
0  3

In 1-D Math, subscripts can be found with crtl-F

In 2-D Math this does not work. 

Also powers of (^) cannot be searched in 2D-Math.

Are there any ways to perfom searches on subscripts or superscripts in 2-D Math?

How do I change the background colour of a workshe...

Asked by: one pound 35
worksheet background color
March 21 2025
2  1

Looking back at this question:

https://www.mapleprimes.com/questions/37691-How-Do-I-Change-The-Background-Colour

the reply by Hmm in 2009

"In Linux there is an X11 resource file for the classic worksheet, one of the settings controls the background color.  The distributed file is located in the maple/X11_defaults directory."

suggested a solution only thiis does not work for me in Maple2024. Perhaps because this worked for the classic view.

Why is there still no way to do this after 16 years or perhaps I just cannot find the option?

Is there away to change the background colour or even invert all colours?

What type of region in my orlsheet?...

Asked by: awass 301
worksheet editing
March 21 2025
0  0

I occasionally find myself inexplicably in a region of my worksheet that does not respond to my editing, fe.g., I cannot erae or I cannot copy. I recently typed a command-there was an error of some form and I tried unsuccessfully to edit it. Then I tried to copy the code and enter it at a prompt. It refused to enter it at the prompt but copied it below the prompt in a strnge region that I do not understand. When I retyped the command at a prompt it worked fine. I do not understand th dead regions that pop up mysteriously. (I am using Maple 2024 on a Mac) The page is too long to copy but I could upload it if given directions.

generate a sequence backwards ...

Asked by: selaf 15
March 13 2025
0  1

I am trying to do something that was recommended in

https://math.stackexchange.com/questions/4583857/how-to-use-recursion-to-define-a-number-series-in-maple

but can't get the desired sequnce. See for example my code

v := proc(m) option remember; return m; end proc;
k := 5:
v(k + 1) := 0:
v(k):=1:
for i from k - 1 by -1 to 1 do
    v(i);
end do;

I get the output 1,1,1,1

I don't get it.

Show steps for viscous Burger's equation...

Asked by: 130
solve
March 11 2025
0  2

Hi!

I am studying Burger's equation, and I would like to see the steps that Maple takes to solve this.  "ShowSteps" doesn't seem to work.

Unfortunately, I am unable to share the worksheet I made.

Server Error - MaplePrimes

 
 

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make faster and explicit way for plotting?...

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performance explore numeric
March 08 2025
4  2

this function i have is so long and my parameter are twenty they are two much when i make a change in explore i the change is so slow and i can't see some of this parameter how act to figure when i change becuase the placement of parameters i want some of parameter being in right  and some of them being in right  and figure be in the middle for see them together can we do something like that?

figure.mw

Is LieAlgebras[Cohomology] broken in Maple 2024.2?...

Asked by: Massimo Bertolotti 5
liealgebra cohomology
March 07 2025
1  0

Hi everyone,

I'm trying to compute the cohomology group of some Lie algebras using the LieAlgebra package, but it appears that the Cohomology command doesn't provide the correct basis for the higher dimensional cohomology group, instead repeating up to the correct dimension only one element.

For example, with the following Lie algebra

L1:=_DG([["LieAlgebra", Alg1, [6]], [[[1, 3, 2], 1], [[1, 2, 3], -1], [[4, 6, 5], 1], [[4, 5, 6], -1]]])
DGSetup(L1)

the command

C := RelativeChains([])

does provide the correct k-forms on Alg1, but then

H := Cohomology(C)
provides
[[theta4,theta1],[theta1 &w theta4, theta1 &w theta4, theta1 &w theta4],[theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3,theta1 &w theta2 &w theta3], [theta1 &w theta2 &w theta3 &w theta4,theta1 &w theta2 &w theta3 &w theta4,theta1 &w theta2 &w theta3 &w theta4],[theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6, theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6], [theta1 &w theta2 &w theta3 &w theta4 &w theta5 &w theta6]

A similar thing does happen for the examples provided in the online help (e.g. example 1 from https://de.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry/LieAlgebras/Cohomology). Is the command broken?

Any help is really appreciated.

what is problem why i can't get result?...

Asked by: salim-barzani 1555
substitution pde differential-equations
March 05 2025
3  2
> 

restart
> 

with(PDEtools)
> 

undeclare(prime, quiet); declare(u(x, y, z, t), quiet); declare(f(x, y, z, t), quiet)

``

 (1)
> 

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

eqw := w[i] = (-1+sqrt(-4*beta*mu*l[i]-4*delta*mu*r[i]-4*mu*k[i]^2-4*alpha*mu+1))/(2*mu)
> 

Bij := proc (i, j) options operator, arrow; -24*mu/(sqrt(1+(-4*beta*l[j]-4*delta*r[j]-4*alpha)*mu)*sqrt(1+(-4*beta*l[i]-4*delta*r[i]-4*alpha)*mu)-1+((2*r[i]+2*r[j])*delta+(2*l[i]+2*l[j])*beta+4*alpha)*mu) end proc
> 

NULL
> 

theta1 := normal(eval(eval(thetai, eqw), i = 1)); theta2 := normal(eval(eval(thetai, eqw), i = 2))
> 

eqf := f(x, y, z, t) = theta1*theta2+Bij(1, 2)
> 

eqfcomplex := collect(evalc(eval(eval(eqf, l[2] = conjugate(l[1])), l[1] = a+I*b)), t)
> 

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; equ := simplify(eval(eq17, eqfcomplex))

So we want to find a substitution that removes the time dependence from u. One way is to find the maximum and see how it moves. Here, the first solution gives what we want.

> 

ans := solve({diff(rhs(equ), x), diff(rhs(equ), y), diff(rhs(equ), z)}, {x, y, z}, explicit)
 

NULL

Download hfz.mw

There is any way for see the outcome of result? fo...

Asked by: salim-barzani 1555
explore substitution plotting
March 05 2025
3  0

i need the result for (eqt33) but i can reach the result there is any  other way for finding? i need to plot 3D of that function but without have the function how i can do explore on it

w1.mw

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