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Re: change a system of PDEs to ODEs via traveling wave

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89010] Re: change a system of PDEs to ODEs via traveling wave
  • From: ToddSmith <elliptic1 at gmail.com>
  • Date: Fri, 23 May 2008 03:10:26 -0400 (EDT)
  • References: <g11r4j$ac8$1@smc.vnet.net> <g134fn$m1r$1@smc.vnet.net>

This works well too:

I use the wave equation:
In[1]:= PDE=D[u[x,t],t,t]==c^2D[u[x,t],x,x]

Out[1]= u^(0,2)[x,t]==c^2 u^(2,0)[x,t]


Define the change of variables as a rule that assigns a pure function
to 'u', and a rule to use the notation
In[2]:= CoV = {u -> (u[#1 - c #2, #1 + c #2] &)};
          newVars = {x - c t -> \[Xi], x + c t -> \[Eta]};

Evaluate the PDE with these rules to get the transformed PDE
In[6]:= tweqn = PDE /. CoV /. newVars;
          Assuming[c > 0, Simplify[tweqn]]

Out[7]= u^(1,1)[\[Xi],\[Eta]]==0


-Todd
http://www.ExampleProblems.com
Graduate level mathematics!!


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