Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F10%3A%230000277" target="_blank" >RIV/47813059:19610/10:#0000277 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

Original language description

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictionson the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the governing equation in terms of elliptic integrals. We show that the instances when the elliptic integrals degenerate to elementary functions were known to nineteenth-century geometers. Finally, we characterize the associated normal congruences.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GP201%2F07%2FP224" target="_blank" >GP201/07/P224: Symbolic computations in the theory of partial differential equations</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Nonlinearity

ISSN

0951-7715

e-ISSN

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Volume of the periodical

23

Issue of the periodical within the volume

10

Country of publishing house

GB - UNITED KINGDOM

Number of pages

21

Pages from-to

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UT code for WoS article

000281377600013

EID of the result in the Scopus database

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