Numerische Analyse äquivarianter
Evolutionsgleichungen
07-069 Wolf-Jürgen Beyn, Vera Thümmler, Sabrina Selle.
Freezing Multipulses and Multifronts
We consider nonlinear time dependent
reaction diffusion systems in one space dimension that exhibit multiple
pulses or multiple fronts. In an earlier paper two of the authors
developed he freezing method that allows to compute a moving
coordinate frame in which, for example, a traveling wave becomes
stationary. In this paper we extend the method to handle multifronts
and multipulses traveling at different speeds. The solution of the
Cauchy problem is decomposed into a finite number of single waves each
of which has its own moving coordinate system. The single solutions
satisfy a system of partial differential algebraic equations coupled
by nonlinear and nonlocal terms. Applications are provided to the
Nagumo and the FitzHugh-Nagumo system. We justify the method by
showing that finitely many traveling waves, when patched together in
an appropriate way, solve the coupled system in an asymptotic
sense. The method is generalized to equivariant evolution equations
and illustrated by the complex Ginzburg Landau equation.
