J. Burke - Center for BioDynamics, Boston University, Boston, MA 02215, United States (email)
Abstract: The one-dimensional Swift-Hohenberg equation is known to exhibit a variety of localized states within the so-called pinning or snaking region. Single-pulse states consist of single localized structures within the spatial domain, and are organized into a snakes-and-ladders structure within the pinning region. Multipulse states consist of two or more localized structures within the domain, but their detailed organization within the pinning region is not known. In this paper we consider multipulse solutions of the one-dimensional Swift-Hohenberg equation on large but periodic domains, and show that while these are also confined to the pinning region the details of their organization depend on whether the pulses are equidistant or not. For large domains the required branch-following becomes delicate and may lead to erroneous results unless performed with great care.
Keywords: Localized states, Swift-Hohenberg equation, homoclinic snaking
Received: September 2008; Revised: March 2009; Published: September 2009.