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