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 -----------------------------------------------