dorsal/arxiv
View SchemaEstabrook-Wahlquist Prolongations and Infinite-Dimensional Algebras
| Authors | J. D. Finley, III |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9512004 |
| URL | https://arxiv.org/abs/solv-int/9512004 |
Abstract
Detailed mappings between zero-curvture equations for prolongation structures of nonlinear pde's and Estabrook-Wahlquist algorithms for same are given. The differences are exemplified by studies of the sine-Gordon equation. An example where the prolongation structure must be infinite-dimensional is given by the Robinson-Trautman equation, where the minimal algebra is $K_2$. In general these algorithms require integration of vector-field valued pde's; solutions of simultaneous flow equations are given. Applications to coupled systems of flow equations are given, where the result describes Lie algebras of vector fields vertical over fibers of pseudopotentials over a jet bundle appropriate for a given system of pde's; algebras invariant under sl(2,C) are of special interest.
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"abstract": "Detailed mappings between zero-curvture equations for prolongation structures\nof nonlinear pde\u0027s and Estabrook-Wahlquist algorithms for same are given. The\ndifferences are exemplified by studies of the sine-Gordon equation. An example\nwhere the prolongation structure must be infinite-dimensional is given by the\nRobinson-Trautman equation, where the minimal algebra is $K_2$. In general\nthese algorithms require integration of vector-field valued pde\u0027s; solutions of\nsimultaneous flow equations are given. Applications to coupled systems of flow\nequations are given, where the result describes Lie algebras of vector fields\nvertical over fibers of pseudopotentials over a jet bundle appropriate for a\ngiven system of pde\u0027s; algebras invariant under sl(2,C) are of special\ninterest.",
"arxiv_id": "solv-int/9512004",
"authors": [
"J. D. Finley",
"III"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Estabrook-Wahlquist Prolongations and Infinite-Dimensional Algebras",
"url": "https://arxiv.org/abs/solv-int/9512004"
},
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