Hi Huisman,
Thanks for your reply. I've just contacted Wolfram technical support, and it should be a
bugHello Guo Zhou,
Thank you for brining this issue to our attention.
I recreated the behavior you described and I found the issue can be seen when only examining the first derivative. Please see the attached notebook for details. I have filed a note with the appropriate members of our development team regardng this.
We are always interested in improving Mathematica and I want to thank you again for taking the time to contact us about this issue. If you have any further questions, or if you find further issues, please feel free to contact us again.
attached notebook
Simplifying issue.
Immediately below is what you found:
u[x_, t_] := InverseFourierTransform[U[k, t], k, x]
D[u[x, t], {x, 2}]
0
D[D[u[x, t], x], x]
InverseFourierTransform[-k^2 U[k, t], k, x]
However, the issue becomes more clear when we see that the first derivative is being handled differently:
D[u[x, t], x]
InverseFourierTransform[-I k U[k, t], k, x]
D[u[x, t], {x, 1}]
0
