Linearizability criteria for systems of two second-order differential equations by complex methods
Abstract Lie’s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinea...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ali, S. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media B.V. 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 66(2011), 1-2 vom: 03. Feb., Seite 77-88 |
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| Übergeordnetes Werk: |
volume:66 ; year:2011 ; number:1-2 ; day:03 ; month:02 ; pages:77-88 |
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| DOI / URN: |
10.1007/s11071-010-9912-2 |
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| 520 | |a Abstract Lie’s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane–Emden type equations which have roots in the study of stellar structures are presented and discussed. | ||
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Abstract Lie’s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane–Emden type equations which have roots in the study of stellar structures are presented and discussed. © Springer Science+Business Media B.V. 2011 |
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Abstract Lie’s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane–Emden type equations which have roots in the study of stellar structures are presented and discussed. © Springer Science+Business Media B.V. 2011 |
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Abstract Lie’s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane–Emden type equations which have roots in the study of stellar structures are presented and discussed. © Springer Science+Business Media B.V. 2011 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC205108923X</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503225121.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2011 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11071-010-9912-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC205108923X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11071-010-9912-2-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ali, S.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Linearizability criteria for systems of two second-order differential equations by complex methods</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2011</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media B.V. 2011</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Lie’s linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing transformations but also the solutions of the nonlinear equations. Here, complex methods for a scalar ordinary differential equation are used for linearizing systems of two second-order ordinary and partial differential equations, which can use the power of the geometric method for writing the solutions. Illustrative examples of mechanical systems including the Lane–Emden type equations which have roots in the study of stellar structures are presented and discussed.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complex linearization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complex Lie symmetries</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lie linearizability</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Mahomed, F. 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