Re: DSolve fails with Telegraph equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg69838] Re: DSolve fails with Telegraph equation*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Mon, 25 Sep 2006 03:52:54 -0400 (EDT)*Organization*: The University of Western Australia*References*: <ef2tha$mmi$1@smc.vnet.net>

In article <ef2tha$mmi$1 at smc.vnet.net>, Oliver Friedrich <xoliver.friedrich at tzm.dex> wrote: > I try to solve the telegraph equation > > dxdx(u[x,t])==A*(u[x,t])+B*dt(u[x,t])+C*dtdt(u[x,t]) > > but DSolve returns immidiately without solution. I thought that this > equation is one of the more easy to crack for Mathematica. Am I wrong? First, it is a bad idea to use single-letter capitals as variables. Second, _which_ solution to the telegraph equation were you expecting? Writing the equation in Mathematica notation as eq = D[u[x, t],{x, 2}] == b D[u[x, t], t] + c D[u[x, t], {t, 2}] + a u[x, t] then one can find traveling-wave solutions via the substitution eq /. u -> Function[{x, t}, f[k x - w t]] /. k x - w t -> z and DSolve[%, f, z] Alternatively, the substitution eq /. u -> Function[{x, t}, Exp[-b t/(2 c)] v[x, t]] (http://eqworld.ipmnet.ru/en/solutions/lpde/lpde207.pdf) leads to the KleinGordon equation. Separable solutions to this equation are given at http://eqworld.ipmnet.ru/en/solutions/lpde/lpde203.pdf Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul