Nonlinear waves in networks: Model reduction for the sine-Gordon equation

Jean Guy Caputo, Denys Dutykh

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

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.

Original languageBritish English
Article number022912
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume90
Issue number2
DOIs
StatePublished - 25 Aug 2014

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