       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:= PDE=D[u[x,t],t,t]==c^2D[u[x,t],x,x]

Out= 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:= 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:= tweqn = PDE /. CoV /. newVars;
Assuming[c > 0, Simplify[tweqn]]

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

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

```

• Prev by Date: Sluggish performance in Save, bug?
• Next by Date: Re: Color space conversion in Mathematica v6.0
• Previous by thread: Re: change a system of PDEs to ODEs via traveling wave
• Next by thread: Color space conversion in Mathematica v6.0