TY - JOUR
AB - 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 the freezing method that allows us 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 systems. 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 is illustrated by the complex Ginzburg-Landau equation.
AU - Beyn, Wolf-Jürgen
AU - Selle, Sabrina
AU - Thümmler, Vera
ID - 1586906
IS - 2
JF - SIAM Journal on Applied Dynamical Systems
KW - multipulses
KW - unbounded
KW - equivariance
KW - domains
KW - Lie groups
KW - partial differential algebraic equations
SN - 1536-0040
TI - Freezing multipulses and multifronts
VL - 7
ER -