Question about changing variables in PDEs

• To: mathgroup at yoda.physics.unc.edu
• Subject: Question about changing variables in PDEs
• From: Scott Herod <sherod at newton.colorado.edu>
• Date: Mon, 26 Oct 92 15:03:33 MST

```	I have a system of PDE's in in three dependent and two independent
variables.  For example:

{ Dt[f,x] + f Dt[g,t] - f g,
Dt[f,x,t] - Dt[h,x]^2,
Dt[g,x] + Dt[h,t]}

In general the equations are much more complicated.

The Dt notation is nice because it is easy to change the
depend variables by simply defining f, g, h in terms of
the new variables.

f = a*k + b*k^2;  SetAttributes[{a,b}, Constant];

is an example.

I would like to do the same with the independent variables but
am having some problem doing this nicely.
The above technique does not work.

Mathematica 2.0 for SPARC
-- X11 windows graphics initialized --

In[1]:= d = Dt[f,x] + Dt[g,x]

Out[1]= Dt[f, x] + Dt[g, x]

In[2]:= x = a+b

Out[2]= a + b

In[3]:= d

General::ivar: a + b is not a valid variable.

General::ivar: a + b is not a valid variable.

Out[3]= Dt[f, a + b] + Dt[g, a + b]

Also using a simply pattern match below doesn't work (bug?).

Mathematica 2.0 for SPARC
-- X11 windows graphics initialized --

In[1]:= d = Dt[f,x] + Dt[g,x]

Out[1]= Dt[f, x] + Dt[g, x]

In[2]:= d /. Dt[y_,x] -> Dt[y,r]

Out[2]= Dt[f, x] + Dt[g, x]

The only way I have of doing this now is making all the replacements by
hand.

In[3]:= d /. Dt[f,x] -> Dt[f,r]

Out[3]= Dt[f, r] + Dt[g, x]

Any suggestions of a technique to make these changes would be
appreciated.

Scott Herod
Applied Mathematics