Error "List encountered within..." in DSolve[ ]?

Questions
,
1

c=310^8
T=0
h=1.0545718 10^(-34)
u={1,0,0,T}/Norm[{1,0,0,T}]
v={0,1,0,T}/Norm[{0,1,0,T}]
a={0,1,0,T} ⋅{0,0,c,T}
b={0,0,1,T} ⋅{0,c,0,T}
d= {0,0,1,T} ⋅{c,0,0,T}
pde =Ih^2(u⋅a-u⋅b)D[psi[x, y,z,t],x] -Ih^2*(u⋅a)D[psi[x, y,z,t],y]+
Ih^2*(u⋅b)* D[psi[x, y,z,t],z]-Ih^2(v⋅d)D[psi[x, y,z,t],z]+
Ih^2*(v⋅d)*(D[psi[x, y,z,t],y]) == 0

Then I try to solve it:

DSolve[pde,{psiT[x,y,z,t],psiX[x,y,z,t],psiY[x,y,z,t],psiZ[x,y,z,t],psiT[x,y,z,t],psiX[x,y,z,t],psiY[x,y,z,t],psiZ[x,y,z,t]},{t,x,y,z}]

But get the message:

“List encountered within <<1>>==0. there should be no list on either side”..

What is the cause of this, and how should I write it correctly?

Thanks

2

Probably the result of preexisting values for some symbols. Try clearing all symbols in the current context and reevaluating the code.

ClearAll[Evaluate[Context[] <> "*"]]
3

Hi Rohit, I found some inconsistencies with cdot and asterisk symbols, after correcting these, I get a working code, but a new and quite different problem:

c=3*10^8
T=2
h=1.0545718* 10^(-34)
u={1,0,0,T}/Norm[{1,0,0,T}]
v={0,1,0,T}/Norm[{0,1,0,T}]
a={0,1,0,T}*{0,0,c,T}
b={0,0,1,T} *{0,c,0,T}
d= {0,0,1,T} *{c,0,0,T}
pde =I*h^2*(u*a-u*b)*D[psi[x, y,z,t],x] -
I*h^2*(u*a)*D[psi[x, y,z,t],y]+I*h^2*(u*b)* D[psi[x, y,z,t],z]-
I*h^2*(v*d)*D[psi[x, y,z,t],z]+I*h^2*(v*d)*(D[psi[x, y,z,t],y]) == 0

Then when solving it:

dsol=DSolve[pde,{psiT[x,y,z,t],psiX[x,y,z,t],psiY[x,y,z,t],psiZ[x,y,z,t],psiT[x,y,z,t],psiX[x,y,z,t],psiY[x,y,z,t],psiZ[x,y,z,t]},{t,x,y,z}];

Supplied equations are not differential or integral equations of the
given functions.

This happens no matter what values the vectors attain.

This should not be the case, if the vectors don’t cancel out.

4

Evaluate the variable pde. You will see the source of the problem.

pde.png
pde.png397×159 2.49 KB

5

As written in the discussion, this problem is there what ever the coefficients are. In your case they give 0=0. If you change them, they don’t give this equality, and still it doesn’t solve. Try this:

c=3*10^8
T=2
h=1.0545718* 10^(-34)
u={1,0,0,T}/Norm[{1,0,0,T}]
v={0,1,0,T}/Norm[{0,1,0,T}]
a={0,1,0,T}*{0,0,c,T}
b={1,1,1,T} *{c,c,c,T}
d= {1,0,1,T} *{c,c,c,T}

    pde =I*h^2*(u*a-u*b)*D[psi[x, y,z,t],x] -
I*h^2*(u*a)*D[psi[x, y,z,t],y]+
I*h^2*(u*b)* D[psi[x, y,z,t],z]-I*h^2*(v*d)*D[psi[x, y,z,t],z]+
I*h^2*(v*d)*(D[psi[x, y,z,t],y]) == 0

    dsol=DSolve[pde,{psiT[x,y,z,t],psiX[x,y,z,t],psiY[x,y,z,t],psiZ[x,y,z,t],
psiT[x,y,z,t],psiX[x,y,z,t],psiY[x,y,z,t],psiZ[x,y,z,t]},{t,x,y,z}];

DSolve", “deqx”, ""Supplied equations are not differential or
integral equations of the given functions.\

So this 0=0 is not the problem. Something else is.