HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Nonlinear waves in networks: model reduction for sine-Gordon

Abstract : To study how nonlinear waves propagate across Y- and T-type junctions, we consider the 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 1D 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 $v > 1 - omega$, where $v$ and $\omega$ are respectively its velocity and frequency. This methodology can be generalized to more complex nonlinear wave models.
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00951705
Contributor : Denys Dutykh Connect in order to contact the contributor
Submitted on : Thursday, November 3, 2016 - 11:58:06 AM
Last modification on : Wednesday, March 2, 2022 - 9:42:12 AM
Long-term archiving on: : Saturday, February 4, 2017 - 12:53:53 PM

Files

JGC_DD-2014.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License

Identifiers

Citation

Jean-Guy Caputo, Denys Dutykh. Nonlinear waves in networks: model reduction for sine-Gordon. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2014, 90, pp.022912. ⟨10.1103/PhysRevE.90.022912⟩. ⟨hal-00951705v3⟩

Share

Metrics

Record views

1419

Files downloads

597