title: Swift-Hohenberg equation with broken reflection symmetry.
abstract: The bistable Swift-Hohenberg equation possesses a variety of time-independent spatially localized solutions organized in the so-called snakes-and-ladders structure. This structure is a consequence of a phenomenon known as homoclinic snaking, and is in turn a consequence of spatial reversibility of the equation. We examine here the consequences of breaking spatial reversibility on the snakes-and-ladders structure. We find that the localized states now drift, and show that the snakes-and-ladders structure breaks up into a stack of isolas. We explore the evolution of this new structure with increasing reversibility breaking and study the dynamics of the system outside of the snaking region using a combination of numerical and analytical techniques.
authors.affiliation: Center for BioDynamics, Boston University, Boston, Massachusetts 02215, USA. jb@math.bu.edu
authors.forename: J
authors.initials: J
authors.lastname: Burke
authors.forename: S M
authors.initials: SM
authors.lastname: Houghton
authors.forename: E
authors.initials: E
authors.lastname: Knobloch
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics