Maps, PDE's and Solitary Waves
solv-int
2015-06-26 v1 chao-dyn
Chaotic Dynamics
Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
patt-sol
Abstract
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing solutions, and elastically colliding solutions. Unlike PDE's, the model can be applied with minimal computational machinery, and few sources of numerical error. Moreover, this model clarifies possible mechanisms by which various coherent solutions are maintained in the face of dispersion.
Cite
@article{arxiv.solv-int/9410002,
title = {Maps, PDE's and Solitary Waves},
author = {Troy Shinbrot and J. M. Ottino},
journal= {arXiv preprint arXiv:solv-int/9410002},
year = {2015}
}
Comments
28 pages, Binhexed Macintosh MS Word 5.1 file follows; available in hardcopy by request (shinbrot@merle.acns.nwu.edu). In press: Int. J. Bif. & Chaos