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MathGroup Archive 1992

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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
Copyright 1988-91 Wolfram Research, Inc.
 -- 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
Copyright 1988-91 Wolfram Research, Inc.
 -- 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
	University of Colorado, Boulder
	(sherod at newton.colorado.edu)





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