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The Riccati and Ermakov-Pinney hierarchies
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- Euler, Marianna (author)
- Luleå tekniska universitet,Matematiska vetenskaper,Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, Auravägen 17, SE-182 60 Djursholm, Sweden
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- Euler, Norbert (author)
- Luleå tekniska universitet,Matematiska vetenskaper,Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, Auravägen 17, SE-182 60 Djursholm, Sweden
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- Leach, Peter (author)
- Institut Mittag-Leffler, The Royal Swedish Academy of Sciences, Auravägen 17, SE-182 60 Djursholm, Sweden; School of Mathematical Sciences, Howard College, University of KwaZulu-Natal, Durban, Republic of South Africa
- (creator_code:org_t)
- 2007
- 2007
- English.
- In: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 14:2, s. 290-302
- Journal article (peer-reviewed)
Abstract
Subject headings
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- The concept and use of recursion operators is well-established in the study of evolution, in particular nonlinear, equations. We demonstrate the application of the idea of recursion operators to ordinary differential equations. For the purposes of our demonstration we use two equations, one chosen from the class of linearisable hierarchies of evolution equations studied by Euler et al (Stud Appl Math 111 (2003) 315-337) and the other from the class of integrable but nonlinearisible equations studied by Petersson et al (Stud Appl Math 112 (2004) 201-225). We construct the hierarchies for each equation. The symmetry properties of the first hierarchy are considered in some detail. For both hierarchies we apply the singularity analysis. For both we observe intersting behaviour of the resonances for the different possible leading order behaviours. In particular we note the proliferation of subsidiary solutions as one ascends the hierarchy.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Matematik
- Mathematics
Publication and Content Type
- ref (subject category)
- art (subject category)
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