Maps, PDE's and Solitary Waves

Details Maps, PDE's and Solitary Waves Maps, PDE's and Solitary Waves

1994-10-13

arxiv.org/abs/solv-int/9410002v1

Nonlinear Sciences

Chaotic Dynamics

28 pages, Binhexed Macintosh MS Word 5.1 file follows; available in hardcopy by request (shinbrot@merle.acns.nwu.edu). In pres

Scientific paper

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.

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