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!!