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Essential variables in the integrability problem of planar vector fields

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Title: Essential variables in the integrability problem of planar vector fields
Authors: Giné, Jaume gine@matematica.udl.cat, Santallusia, Xavier1 xsantall@xtec.cat
Source: Physics Letters A. Jan2011, Vol. 375 Issue 3, p291-297. 7p.
Subjects: Nonlinear differential equations, Calculus problems & exercises, Mathematical variables, Vector fields, Integrals, Mathematical series
Abstract: Abstract: This Letter is devoted to the integrability problem of planar nonlinear differential equations. We introduce a new method to detect local analytic integrability or to construct a singular series expansion of the first integral around a singular point for planar vector fields. The method allows to find new variables (essential variables) where the integrability problem is more feasible. The new method can be used in different context and is an alternative to all the methods developed up to now for any particular case. [ABSTRACT FROM AUTHOR]
Copyright of Physics Letters A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 57162894
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Essential variables in the integrability problem of planar vector fields
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  Data: Abstract: This Letter is devoted to the integrability problem of planar nonlinear differential equations. We introduce a new method to detect local analytic integrability or to construct a singular series expansion of the first integral around a singular point for planar vector fields. The method allows to find new variables (essential variables) where the integrability problem is more feasible. The new method can be used in different context and is an alternative to all the methods developed up to now for any particular case. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Physics Letters A is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.physleta.2010.11.026
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      – Code: eng
        Text: English
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        PageCount: 7
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    Subjects:
      – SubjectFull: Nonlinear differential equations
        Type: general
      – SubjectFull: Calculus problems & exercises
        Type: general
      – SubjectFull: Mathematical variables
        Type: general
      – SubjectFull: Vector fields
        Type: general
      – SubjectFull: Integrals
        Type: general
      – SubjectFull: Mathematical series
        Type: general
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      – TitleFull: Essential variables in the integrability problem of planar vector fields
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            NameFull: Giné, Jaume
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              Text: Jan2011
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