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mskalsi

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These are questions asked by mskalsi

Are there any Maple trainling programme ...

mskalsi 290 Maple
September 21 2016
1 0

Can anybody please tell, where I can find seminar/workshops on Maple training ?

Regards

How I can use Differential Algebra packa...

mskalsi 290 Maple 18
pdetools
September 09 2016
1 2

Dear All

I need to reduce system of differential equation system into triangular system which I came to know can be done using Maple package "DifferentialAlgebra", but I do not know how to use this package for triangularization.

The differential system is DetSys derived from  some PDE:

 

> 

with(PDEtools):
> 

DepVars := [f(u(x, t)), u(x, t)]; 1; declare(f(u(x, t)), u(x, t))

[f(u(x, t)), u(x, t)]

  

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

  

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

 (1)
> 

PDE1 := diff(u(x, t), t, t)-(diff(u(x, t), x, x))-f(u) = 0

diff(diff(u(x, t), t), t)-(diff(diff(u(x, t), x), x))-f(u) = 0

 (2)
> 

G := [xi(x, t, u), tau(x, t, u), phi(x, t, u)]

[xi(x, t, u), tau(x, t, u), phi(x, t, u)]

 (3)
> 

declare(G)

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

  

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

  

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

 (4)
> 

DetSys := DeterminingPDE(PDE1, G, integrabilityconditions = false)

{-2*(diff(diff(tau(x, t, u), t), u))+diff(diff(phi(x, t, u), u), u), 2*(diff(diff(tau(x, t, u), u), x))-2*(diff(diff(xi(x, t, u), t), u)), 2*(diff(diff(xi(x, t, u), u), x))-(diff(diff(phi(x, t, u), u), u)), 2*(diff(tau(x, t, u), x))-2*(diff(xi(x, t, u), t)), 2*(diff(xi(x, t, u), x))-2*(diff(tau(x, t, u), t)), diff(diff(tau(x, t, u), x), x)+2*(diff(diff(phi(x, t, u), t), u))-(diff(diff(tau(x, t, u), t), t))-3*(diff(tau(x, t, u), u))*f(u), diff(diff(xi(x, t, u), x), x)-2*(diff(diff(phi(x, t, u), u), x))-(diff(diff(xi(x, t, u), t), t))-f(u)*(diff(xi(x, t, u), u)), -(diff(diff(phi(x, t, u), x), x))+diff(diff(phi(x, t, u), t), t)-phi(x, t, u)*(diff(f(u), u))+(diff(phi(x, t, u), u))*f(u)-2*(diff(tau(x, t, u), t))*f(u), diff(diff(tau(x, t, u), u), u), diff(diff(xi(x, t, u), u), u), diff(tau(x, t, u), u), diff(xi(x, t, u), u)}

 (5)
> 

for EQ in sort([op(DetSys)], length) do EQ = 0 end do:

 

 

Download [1117]_Symmetries_determination.mw

Regards

Is my way finding symmetries is correct ...

mskalsi 290 Maple 18
symmetry
September 05 2016
0 0

Dear All

In following I tried to find symmetries of certain partial differential equation taken from paper "Group classification and exact solutions of generalized modified Boussinesq equation". But the determining equations are not matching with equations obtained in paper.


> 

with(PDEtools)
> 

DepVars := [f(u(x, t)), u(x, t)]; declare(f(u(x, t)), u(x, t))

[f(u(x, t)), u(x, t)]

  

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

  

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

 (1)
> 

PDE1 := diff(u(x, t), t, t)-delta*(diff(u(x, t), x, x, t, t))-(diff(f(u(x, t)), x, x))

diff(diff(u(x, t), t), t)-delta*(diff(diff(diff(diff(u(x, t), t), t), x), x))-((D@@2)(f))(u(x, t))*(diff(u(x, t), x))^2-(D(f))(u(x, t))*(diff(diff(u(x, t), x), x))

 (2)
> 

G := [seq(xi[j](x, t, u), j = [x, t]), seq(eta[j](x, t, u), j = [u])]

[xi[x](x, t, u), xi[t](x, t, u), eta[u](x, t, u)]

 (3)
> 

declare(G)

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

  

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

 (4)
> 

DetSys := DeterminingPDE(PDE1, G, integrabilityconditions = false)

{diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta, (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)), 2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)), 2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)), 4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t), 2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta, -(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), -2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta, 2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta, diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta, 2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta, -(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta, -(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta, -2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta, (diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)), 2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta, diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u), diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x), diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u), diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), u), diff(diff(diff(xi[t](x, t, u), u), u), x), diff(diff(diff(xi[t](x, t, u), u), x), x), diff(diff(diff(xi[x](x, t, u), t), t), u), diff(diff(diff(xi[x](x, t, u), t), u), u), diff(diff(diff(xi[x](x, t, u), u), u), u), diff(diff(xi[t](x, t, u), u), u), diff(diff(xi[t](x, t, u), u), x), diff(diff(xi[t](x, t, u), x), x), diff(diff(xi[x](x, t, u), t), t), diff(diff(xi[x](x, t, u), t), u), diff(diff(xi[x](x, t, u), u), u), diff(xi[t](x, t, u), u), diff(xi[t](x, t, u), x), diff(xi[x](x, t, u), t), diff(xi[x](x, t, u), u)}

 (5)
> 

for EQ in sort([op(DetSys)], length) do EQ = 0 end do

diff(xi[t](x, t, u), u) = 0

  

diff(xi[t](x, t, u), x) = 0

  

diff(xi[x](x, t, u), t) = 0

  

diff(xi[x](x, t, u), u) = 0

  

diff(diff(xi[t](x, t, u), u), u) = 0

  

diff(diff(xi[t](x, t, u), u), x) = 0

  

diff(diff(xi[t](x, t, u), x), x) = 0

  

diff(diff(xi[x](x, t, u), t), t) = 0

  

diff(diff(xi[x](x, t, u), t), u) = 0

  

diff(diff(xi[x](x, t, u), u), u) = 0

  

diff(diff(diff(xi[t](x, t, u), u), u), u) = 0

  

diff(diff(diff(xi[t](x, t, u), u), u), x) = 0

  

diff(diff(diff(xi[t](x, t, u), u), x), x) = 0

  

diff(diff(diff(xi[x](x, t, u), t), t), u) = 0

  

diff(diff(diff(xi[x](x, t, u), t), u), u) = 0

  

diff(diff(diff(xi[x](x, t, u), u), u), u) = 0

  

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), u) = 0

  

diff(diff(diff(diff(xi[t](x, t, u), u), u), u), x) = 0

  

diff(diff(diff(diff(xi[x](x, t, u), t), u), u), u) = 0

  

diff(diff(diff(diff(xi[x](x, t, u), u), u), u), u) = 0

  

diff(diff(xi[t](x, t, u), u), u)-(diff(diff(diff(diff(xi[t](x, t, u), u), u), x), x))*delta = 0

  

4*(diff(diff(xi[x](x, t, u), t), x))-2*(diff(diff(eta[u](x, t, u), t), u))+diff(diff(xi[t](x, t, u), t), t) = 0

  

2*(diff(diff(xi[x](x, t, u), u), x))+2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u)) = 0

  

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x))+4*(diff(diff(xi[t](x, t, u), t), x)) = 0

  

2*(diff(diff(diff(xi[x](x, t, u), u), u), x))+2*(diff(diff(diff(xi[t](x, t, u), t), u), u))-(diff(diff(diff(eta[u](x, t, u), u), u), u)) = 0

  

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), x), x))*delta = 0

  

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

  

2*(diff(diff(diff(diff(xi[x](x, t, u), u), u), u), x))+2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), u))-(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), u)) = 0

  

-(diff(diff(xi[x](x, t, u), u), u))*(diff(f(u), u))-(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[x](x, t, u), u)) = 0

  

-(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta-4*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+2*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(xi[x](x, t, u), u)) = 0

  

2*(diff(xi[x](x, t, u), u))-8*(diff(diff(diff(xi[t](x, t, u), t), u), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), u), u), x))*delta-2*(diff(diff(diff(xi[x](x, t, u), u), x), x))*delta = 0

  

2*(diff(diff(xi[t](x, t, u), t), u))-(diff(diff(eta[u](x, t, u), u), u))+(diff(diff(diff(diff(eta[u](x, t, u), u), u), x), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), u), x), x))*delta = 0

  

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta-2*(diff(diff(diff(xi[x](x, t, u), t), t), x))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

  

-2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+4*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-2*(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-8*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

  

2*(diff(xi[t](x, t, u), u))*(diff(f(u), u))+2*delta*(diff(diff(diff(eta[u](x, t, u), t), u), u))-(diff(diff(diff(xi[t](x, t, u), t), t), u))*delta-4*(diff(diff(diff(xi[x](x, t, u), t), u), x))*delta = 0

  

diff(diff(xi[x](x, t, u), u), u)-4*(diff(diff(diff(diff(xi[t](x, t, u), t), u), u), x))*delta+2*(diff(diff(diff(diff(eta[u](x, t, u), u), u), u), x))*delta-(diff(diff(diff(diff(xi[x](x, t, u), u), u), x), x))*delta = 0

  

-2*(diff(xi[t](x, t, u), x))*(diff(f(u), u))+2*(diff(xi[x](x, t, u), t))-2*(diff(diff(diff(xi[x](x, t, u), t), x), x))*delta+4*(diff(diff(diff(eta[u](x, t, u), t), u), x))*delta-2*(diff(diff(diff(xi[t](x, t, u), t), t), x))*delta = 0

  

-(diff(diff(xi[t](x, t, u), x), x))*(diff(f(u), u))+diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), x), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), x), x))*delta = 0

  

-(diff(diff(xi[t](x, t, u), u), u))*(diff(f(u), u))-4*(diff(diff(diff(diff(xi[x](x, t, u), t), u), u), x))*delta-(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), u))*delta+(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), u))+2*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), u))*delta = 0

  

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))+diff(diff(xi[x](x, t, u), t), t)-delta*(diff(diff(diff(diff(xi[x](x, t, u), t), t), x), x))+2*delta*(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), x)) = 0

  

2*(diff(diff(xi[x](x, t, u), t), u))-2*(diff(diff(xi[t](x, t, u), u), x))*(diff(f(u), u))-2*(diff(xi[t](x, t, u), x))*(diff(diff(f(u), u), u))+4*(diff(diff(diff(diff(eta[u](x, t, u), t), u), u), x))*delta-2*(diff(diff(diff(diff(xi[t](x, t, u), t), t), u), x))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), u), x), x))*delta = 0

  

(diff(diff(diff(diff(eta[u](x, t, u), t), t), u), u))*delta-2*(diff(diff(diff(diff(xi[x](x, t, u), t), t), u), x))*delta+(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+(diff(diff(eta[u](x, t, u), u), u))*(diff(f(u), u))-2*(diff(diff(xi[x](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t)+(1/2)*(diff(eta[u](x, t, u), u))) = 0

 (6)
> 

DetSys1 := dsubs(diff(xi[t](x, t, u), u) = 0, diff(xi[t](x, t, u), x) = 0, diff(xi[x](x, t, u), t) = 0, diff(xi[x](x, t, u), u) = 0, diff(eta[u](x, t, u), u, u) = 0, diff(eta[u](x, t, u), x, u, t) = 0, DetSys)

{0, diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)), diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)), -2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta, (diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)), (diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)), (diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)), -(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x))}

 (7)
> 

for EQ in sort([op(DetSys1)], length) do EQ = 0 end do

0 = 0

  

diff(diff(xi[t](x, t, u), t), t)-2*(diff(diff(eta[u](x, t, u), t), u)) = 0

  

diff(diff(xi[x](x, t, u), x), x)-2*(diff(diff(eta[u](x, t, u), u), x)) = 0

  

-2*(diff(xi[x](x, t, u), x))+(diff(diff(diff(eta[u](x, t, u), u), x), x))*delta = 0

  

(diff(diff(f(u), u), u))*eta[u](x, t, u)+(diff(diff(diff(eta[u](x, t, u), t), t), u))*delta+2*(diff(xi[t](x, t, u), t))*(diff(f(u), u)) = 0

  

(diff(diff(eta[u](x, t, u), x), x))*(diff(f(u), u))+(diff(diff(diff(diff(eta[u](x, t, u), t), t), x), x))*delta-(diff(diff(eta[u](x, t, u), t), t)) = 0

  

(diff(diff(diff(f(u), u), u), u))*eta[u](x, t, u)+2*(diff(diff(f(u), u), u))*(diff(xi[t](x, t, u), t))+(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), u)) = 0

  

-(diff(diff(xi[x](x, t, u), x), x))*(diff(f(u), u))+2*(diff(diff(eta[u](x, t, u), u), x))*(diff(f(u), u))+2*(diff(diff(f(u), u), u))*(diff(eta[u](x, t, u), x)) = 0

 (8)

The third equation in (8) can simplify last equation. This will give us eta[u][x] = 0as f[u, u] is non zero.

> 

NULL


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How to find selected coefficient in Diff...

mskalsi 290 Maple 18
coefficients
August 11 2016
3 9

How I can find coefficient of g(z)^-2, g(z)^4 in differential expression ?


> 

with(PDEtools):
> 

(diff(g(z), x))*g(z)^3+(diff(g(z), z, z))*g(z)^4+(diff(g(z), z, z, z))*g(z)^5+(diff(g(z), z))/g(z)^2

(diff(diff(g(z), z), z))*g(z)^4+(diff(diff(diff(g(z), z), z), z))*g(z)^5+(diff(g(z), z))/g(z)^2

 (1)
> 

dcoeffs((diff(diff(g(z), z), z))*g(z)^4+(diff(diff(diff(g(z), z), z), z))*g(z)^5+(diff(g(z), z))/g(z)^2, g(z))

1, 1, 1/g(z)^2

 (2)
> 

dcoeffs((diff(diff(g(z), z), z))*g(z)^4+(diff(diff(diff(g(z), z), z), z))*g(z)^5+(diff(g(z), z))/g(z)^2, g(z)^4)

Error, invalid input: PDEtools:-dcoeffs expects its 2nd argument, V, to be of type {`PDEtools/F(x,...)`, And(function, `ODEtools/F(x)`)}, but received g(z)^4

  
> 

coeff((diff(diff(g(z), z), z))*g(z)^4+(diff(diff(diff(g(z), z), z), z))*g(z)^5+(diff(g(z), z))/g(z)^2, g(z)^2)

Error, unable to compute coeff

  
> 

coeff((diff(diff(g(z), z), z))*g(z)^4+(diff(diff(diff(g(z), z), z), z))*g(z)^5+(diff(g(z), z))/g(z)^2, 1/g(z))

Error, unable to compute coeff

  
> 

``


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How I can separate real and imaginary pa...

mskalsi 290 Maple 18
July 25 2016
1 0


Suppose I have a PDE

> 

i*psi[t]+psi[xx] = epsilon*(abs(psi)^2)[yy]*psi:

Here I can set psi = u(x, y, t)+i*v(x, y, t), i = sqrt(-1)

Then my query is, how can I obtain simplified resultant system after equating real and imaginary parts. Of course there would be two partial differential equations in u(x, y, t)and v(x, y, t) and those can also be written down manually very easily but this process becomes difficult when we have large system.

Please help !!!


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