On integrability of Weingarten surfaces: a forgotten class
Result description
Rediscovered by a systematic search, a forgotten class of integrable surfaces is shown to disprove the Finkel-Wu conjecture. The associated integrable nonlinear partial differential equation z(yy) + (1/z)(xx) + 2 = 0 possesses a zero curvature representation, a third-order symmetry and a nonlocal transformation to the sine-Gordon equation phi(xi eta) = sin phi. We leave open the problem of finding a Backlund autotransformation and a recursion operator that would produce a local hierarchy.
Keywords
integrable surfacesWeingarten surfacesFinkel?Wu conjecturezero curvature representationsurfaces of constant astigmatism
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On integrability of Weingarten surfaces: a forgotten class
Original language description
Rediscovered by a systematic search, a forgotten class of integrable surfaces is shown to disprove the Finkel-Wu conjecture. The associated integrable nonlinear partial differential equation z(yy) + (1/z)(xx) + 2 = 0 possesses a zero curvature representation, a third-order symmetry and a nonlocal transformation to the sine-Gordon equation phi(xi eta) = sin phi. We leave open the problem of finding a Backlund autotransformation and a recursion operator that would produce a local hierarchy.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GP201/07/P224: Symbolic computations in the theory of partial differential equations
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A: Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
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Volume of the periodical
42
Issue of the periodical within the volume
40
Country of publishing house
GB - UNITED KINGDOM
Number of pages
16
Pages from-to
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UT code for WoS article
000269876700008
EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2009