dorsal/arxiv
View SchemaMaps, PDE's and Solitary Waves
| Authors | Troy Shinbrot, J. M. Ottino |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9410002 |
| URL | https://arxiv.org/abs/solv-int/9410002 |
| DOI | 10.1142/S0218127495000429 |
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.
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"date_created": "2026-03-02T18:02:48.371000Z",
"date_modified": "2026-03-02T18:02:48.371000Z",
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"abstract": "We describe a map-based model which reproduces many of the behaviors seen in\npartial differential equations (PDE\u0027s). Like PDE\u0027s, we show that this model can\nsupport an infinite number of stationary solutions, traveling solutions,\nbreathing solutions, and elastically colliding solutions. Unlike PDE\u0027s, the\nmodel can be applied with minimal computational machinery, and few sources of\nnumerical error. Moreover, this model clarifies possible mechanisms by which\nvarious coherent solutions are maintained in the face of dispersion.",
"arxiv_id": "solv-int/9410002",
"authors": [
"Troy Shinbrot",
"J. M. Ottino"
],
"categories": [
"solv-int",
"chao-dyn",
"nlin.CD",
"nlin.PS",
"nlin.SI",
"patt-sol"
],
"doi": "10.1142/S0218127495000429",
"title": "Maps, PDE\u0027s and Solitary Waves",
"url": "https://arxiv.org/abs/solv-int/9410002"
},
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"execution_id": "d77e0e8f-9dde-430f-830e-24a2dc75d53e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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