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


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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