title: Nonlinear waves in networks: model reduction for the sine-Gordon equation.
abstract: To study how nonlinear waves propagate across Y- and T-type junctions, we consider the two-dimensional (2D) sine-Gordon equation as a model and examine the crossing of kinks and breathers. Comparing energies for different geometries reveals that, for small widths, the angle of the fork plays no role. Motivated by this, we introduce a one-dimensional effective model whose solutions agree well with the 2D simulations for kink and breather solutions. These exhibit two different behaviors: a kink crosses if it has sufficient energy; conversely a breather crosses when v>1-ω, where v and ω are, respectively, its velocity and frequency. This methodology can be generalized to more complex nonlinear wave models.
authors.affiliation: Laboratoire de Mathématiques, INSA de Rouen, 76801 Saint-Etienne du Rouvray, France.
authors.forename: Jean-Guy
authors.initials: JG
authors.lastname: Caputo
authors.affiliation: LAMA, UMR 5127 CNRS, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France.
authors.forename: Denys
authors.initials: D
authors.lastname: Dutykh
mesh_terms: D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics