DSolve?? solution which is not a solution

• To: mathgroup at smc.vnet.net
• Subject: [mg28753] DSolve?? solution which is not a solution
• From: Marco Beleggia <beleggia at df.unibo.it>
• Date: Fri, 11 May 2001 20:00:31 -0400 (EDT)
• Organization: Physics Department and INFM, University of Bologna
• Sender: owner-wri-mathgroup at wolfram.com

```I have a homogeneous differential equation for a vector
(physically speaking it is a vector potential):

a-T.Laplacian[a]==0    (1)

where T is a diagonal 3x3 matrix of diagonal elements l^2{1,1,G}

and the condition of vanishing divergence for the same vector:

Div[a]==0     (2)

The vector is written in a 2D Fourier-space (q,p), as:

a={ax[q,p,z],ay[q,p,z],az[q,p,z]} Exp[I q x+I p y]    (3)

I create a system with the three components of eq.(1) and
the additional eq.(2), and employ DSolve to find a general solution.

Matemhatica (4.0 for Mac) gives me a solution, which I call "asol".

The problem is: when I verify the solution, inserting "asol"
in eq.(1), I find that the solution is not valid. In
particular, the result of the verification

asol-T.Laplacian[asol]

is a vector

{0,0,something}

which is not equal to {0,0,0} as it should be.

Instead, the verification of eq.(2) is OK:

Div[asol]==0

Somebody can help me to understand what's wrong?

I can send the notebook to anybody, if necessary.

Thank you very much

Marco

--
-----------------------------------------------
Marco Beleggia, PostDoc
Dipartimento di Fisica and INFM
Universita' di Bologna
V.le B.Pichat 6/2, 40127 Bologna, Italy
tel: +390512095147
fax: +390512095153
-----------------------------------------------

```

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