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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88953] Re: change a system of PDEs to ODEs via traveling wave
  • From: Julian Aguirre <julian.aguirre at ehu.es>
  • Date: Thu, 22 May 2008 02:36:22 -0400 (EDT)
  • References: <g11r4j$ac8$1@smc.vnet.net>

Todd,

On 21 mayo, 20:54, ToddSmith <ellipt... at gmail.com> wrote:
> Hi,
>  If I have a system of PDEs in x and t, how can I change to the
> traveling wave variable xi=x-ct to get a system of ODEs?

This is an example for Burger's equation

u_t -u_xx + u u_x = 0 .

It should be easy to extend it to a system. Define the operator

burgers[u_, {x_,t_}] := D[u,x] - D[u, {x,2}] + u D[u, {x,2}]

Now

burgers[f[x - c t], {x,t}] /. x - c t -> y

gives the equation for a travelling wave with profile f[y].

Julian


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