dorsal/arxiv
View SchemaAlgorithms for the Nonclassical Method of Symmetry Reductions
| Authors | Peter A. Clarkson, Elizabeth L. Mansfield |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9401002 |
| URL | https://arxiv.org/abs/solv-int/9401002 |
Abstract
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This algorithm requires significantly less computation time than that standardly used, and avoids many of the difficulties commonly encountered. The proof of correctness of the algorithm is a simple application of the theory of Grobner bases. In the second part we demonstrate some algorithms which may be used to analyse, and often to solve, the resulting systems of overdetermined nonlinear PDEs. We take as our principal example a generalised Boussinesq equation, which arises in shallow water theory. Although the equation appears to be non-integrable, we obtain an exact ``two-soliton'' solution from a nonclassical reduction.
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"abstract": "In this article we present first an algorithm for calculating the determining\nequations associated with so-called ``nonclassical method\u0027\u0027 of symmetry\nreductions (a la Bluman and Cole) for systems of partial differentail\nequations. This algorithm requires significantly less computation time than\nthat standardly used, and avoids many of the difficulties commonly encountered.\nThe proof of correctness of the algorithm is a simple application of the theory\nof Grobner bases. In the second part we demonstrate some algorithms which may\nbe used to analyse, and often to solve, the resulting systems of overdetermined\nnonlinear PDEs. We take as our principal example a generalised Boussinesq\nequation, which arises in shallow water theory. Although the equation appears\nto be non-integrable, we obtain an exact ``two-soliton\u0027\u0027 solution from a\nnonclassical reduction.",
"arxiv_id": "solv-int/9401002",
"authors": [
"Peter A. Clarkson",
"Elizabeth L. Mansfield"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Algorithms for the Nonclassical Method of Symmetry Reductions",
"url": "https://arxiv.org/abs/solv-int/9401002"
},
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