[?] Use a delayed rule to substitute a multi-variable derivative?

Questions
1

I was using a delayed rule to substitute a multi-variable derivative, but syntax error encountered in my second input as the following and the attachments. I am a Newbie. Is there anyone who would like to tell me what’s wrong and how to fix it? Thanks a lot!

kc1 = -\!\(
\*SubscriptBox[\(\[PartialD]\), \(t\)]\(\[Eta][x, t]\)\) - U1 \!\(
\*SubscriptBox[\(\[PartialD]\), \(x\)]\(\[Eta][x, t]\)\) + \!\(
\*SubscriptBox[\(\[PartialD]\), \(y\)]\(
\(\*SubscriptBox[\(\[Phi]\), \(1\)]\)[x, y, t]\)\)

temp1 = kc1 /. {(\[Eta]^(a1_, a2_))[x, t] :> \!\(
\*SubscriptBox[\(\[PartialD]\), \({x, a1}, {t, a2}\)]\((
\*OverscriptBox[\(\[Eta]\), \(^\)] Exp[I\ k \((x - ct)\)])\)\)}
2

Hi Leshan,

take a look at FullForm[kc1] to see how the expression is actually coded:

FullForm[kc1]

From there you can derive how the rule should look:

temp1 = kc1 /. 
  Derivative[a1_, a2_][\[Eta]][x, t] :> 
   OverHat[\[Eta]] D[Exp[I k (x - c t)], {x, a1}, {t, a2}]

Regards,
Michael

3

@Leshan Fisher please make sure you know the rules: https://wolfr.am/READ-1ST

In future attach actual notebook .nb files, and NOT the .pdf files.

4

Thank you Michael for your help! Now I know that there are different forms of a mathematic formula in Mathematica, and that one cannot input a partial derivative from the Pallettes using such a traditional form as superscript enclosed by parentheses.

Best Regards

Leshan Fisher

5

Thanks for your reminding! I have read the rules as you suggested, and won’t attach .pdf files again.

Best Regards, Leshan Fisher