Advanced Search

salim-barzani

950 Reputation

8 Badges

0 years, 283 days
Contact salim-barzani

MaplePrimes Activity


These are questions asked by salim-barzani

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

salim-barzani 950 Maple 2024
substitution pde differential-equations
March 05 2025
0 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 ...

salim-barzani 950 Maple 2024
explore substitution plotting
March 05 2025
0 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

How i can reach the result by applying s...

salim-barzani 950 Maple 2024
substitution pde differential-equations
March 01 2025
0 0

 always i try to apply a technique like long wave limit to get my result, but this time when i do i reach zero so the author try to use another method which really i can't reach how they did and some term are dispear and some are remain , it about substituting and apply epsilon go to zero which i don't know how they apply, anyone can figure out how they reach the result, and maybe my letter and paper are not same about small and capital but it is so clear 

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

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

 (1)
> 

_local(gamma)
> 

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)
> 

NULL
> 

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))+gamma*(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)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

 (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)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z)), 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)
> 

lambda := 1; alpha := 1; beta := 1; gamma := 1

1

  

1

  

1

  

1

 (6)
> 

NULL
> 

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

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

 (7)
> 

NULL
> 

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

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

 (8)
> 

NULL
> 

Bij := proc (i, j) options operator, arrow; (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) end proc

proc (i, j) options operator, arrow; (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) end proc

 (9)
> 

NULL
> 

eij := (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)

(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)

 (10)
> 

eval(eij, k[j] = b*k[i]); series(%, k[i], 3); convert(%, polynom); eval(%, b = k[j]/k[i]); Bij := (%-1)/(k[i]*k[j])

(3*k[i]^6*b^2-6*k[i]^6*b^3+(3*b^4*k[i]^4+l[j]^2)*k[i]^2-2*k[i]^2*b*l[i]*l[j]+b^2*k[i]^2*l[i]^2)/(3*k[i]^6*b^2+6*k[i]^6*b^3+(3*b^4*k[i]^4+l[j]^2)*k[i]^2-2*k[i]^2*b*l[i]*l[j]+b^2*k[i]^2*l[i]^2)

  

series(1+O(k[i]^4),k[i],4)

  

1

  

1

  

0

 (11)
> 

NULL


Download transformation.mw

there is any way to use explicate for re...

salim-barzani 950 Maple 2024
pde explicit differential-equations
February 28 2025
1 1

I want to remove the Lambert function (LambertW) from my equation, but I don't know how. I tried using the explicit option, but it didn't work. How can I express the equation without LambertW?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

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), `$`(x, 3)), x)-lambda*(diff(u(x, y, z, t), `$`(y, 2)))+diff(alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+gamma*(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)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

 (4)
> 

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

0, 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)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

 (5)
> 

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

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

  

w[i]*k[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+12*k[i]^2*(exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]))^2+k[i]^4*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])-lambda*l[i]^2*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+alpha*k[i]^2*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+beta*k[i]*l[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+gamma*k[i]*r[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])

  

w[i] = -(t*k[i]^4+gamma*t*k[i]*r[i]+alpha*t*k[i]^2+beta*t*k[i]*l[i]-lambda*t*l[i]^2+LambertW(12*t*k[i]*exp(-(t*k[i]^4+alpha*t*k[i]^2+beta*t*k[i]*l[i]+gamma*t*k[i]*r[i]-lambda*t*l[i]^2-x*k[i]^2-y*k[i]*l[i]-z*k[i]*r[i]-eta[i]*k[i])/k[i]))*k[i])/(t*k[i])

 (6)
> 

sol := solve(eq15, w[i], explicit)

-(t*k[i]^4+gamma*t*k[i]*r[i]+alpha*t*k[i]^2+beta*t*k[i]*l[i]-lambda*t*l[i]^2+LambertW(12*t*k[i]*exp(-(t*k[i]^4+alpha*t*k[i]^2+beta*t*k[i]*l[i]+gamma*t*k[i]*r[i]-lambda*t*l[i]^2-x*k[i]^2-y*k[i]*l[i]-z*k[i]*r[i]-eta[i]*k[i])/k[i]))*k[i])/(t*k[i])

 (7)
 

NULL

Download remove.mw

How define the PDE which contain integr...

salim-barzani 950 Maple 2024
pde differential-equations duplicate-question
February 21 2025
0 10

i try find some part of solution of this kind of pde but i can't get results my openion is maybe this pde is wronge when i defined 

pde.mw

3 4 5 6 7 8 9 Last Page 5 of 25