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The proof of correctness of the algorithm is a simple application of the theory of Grobner bases.<\/jats:p>\n                  <jats:p>In the second part they demonstrate some algorithms which may be used to analyse, and often to solve, the resulting systems of overdetermined nonlinear PDEs. The authors take as their principal example a generalised Boussinesq equation, which arises in shallow water theory. Although the equation appears to be nonintegrable, the authors obtain an exact \u201ctwo-soliton\u201d solution from a nonclassical reduction.<\/jats:p>","DOI":"10.1137\/s0036139993251846","type":"journal-article","created":{"date-parts":[[2005,2,23]],"date-time":"2005-02-23T09:56:44Z","timestamp":1109152604000},"page":"1693-1719","source":"Crossref","is-referenced-by-count":104,"title":["Algorithms for the Nonclassical Method of Symmetry Reductions"],"prefix":"10.1137","volume":"54","author":[{"given":"Peter A.","family":"Clarkson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elizabeth L.","family":"Mansfield","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970913"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1063\/1.530365"},{"key":"R3","first-page":"19","volume":"40","author":"Bachmair L.","year":"1976","journal-title":"ACM SIGSAM Bulletin"},{"key":"R4","volume-title":"Computational Algebraic Geometry, Part One: Basic Tools","author":"Bayer D.","year":"1986"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-87-05517-7"},{"key":"R6","unstructured":"D. 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