(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Zelik, Sergey; Mielke, Alexander
We study semilinear parabolic systems on the full space Rn that admit a
family of exponentially decaying pulse-like steady states obtained via
translations. The multi-pulse solutions under consideration look like the sum
of infinitely many such pulses which are well separated. We prove a global
center-manifold reduction theorem for the temporal evolution of such
multi-pulse solutions and show that the dynamics of these solutions can be
described by an infinite systems of ODEs for the positions of the pulses. As
an application of the developed theory, we verify the existence of
Sinai-Bunimovich space-time chaos in 1D space-time periodically forced
Swift-Hohenberg equation.
