Strong Embeddability of Time-Invariant Nonlinear Differential Systems in Linear Differential Systems
We consider a pair (Σ, w ) consisting of a time-invariant nonlinear differential system Σ and a real piecewise smooth function w defined on the state space of the differential system. The notion of strong embeddability of the pair (Σ, w ) in a linear differential system is introduced. A criterion fo...
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| Veröffentlicht in: | Differential equations 2019-03, Vol.55 (3), p.303-312 |
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| container_title | Differential equations |
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| creator | Borukhov, V. T. |
| description | We consider a pair (Σ,
w
) consisting of a time-invariant nonlinear differential system Σ and a real piecewise smooth function
w
defined on the state space of the differential system. The notion of strong embeddability of the pair (Σ,
w
) in a linear differential system is introduced. A criterion for the finite-dimensional-strong embeddability of the pair is obtained, linear embedding systems are described, and the explicit representation of first integrals is given for systems in finite-dimensional-strongly embeddable pairs. The class of first integrals determining the general solution of a finite-dimensional-strongly embeddable pair is singled out. |
| doi_str_mv | 10.1134/S0012266119030030 |
| format | Article |
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w
) consisting of a time-invariant nonlinear differential system Σ and a real piecewise smooth function
w
defined on the state space of the differential system. The notion of strong embeddability of the pair (Σ,
w
) in a linear differential system is introduced. A criterion for the finite-dimensional-strong embeddability of the pair is obtained, linear embedding systems are described, and the explicit representation of first integrals is given for systems in finite-dimensional-strongly embeddable pairs. The class of first integrals determining the general solution of a finite-dimensional-strongly embeddable pair is singled out.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266119030030</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Difference and Functional Equations ; Embedded systems ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equation ; Ordinary Differential Equations ; Partial Differential Equations</subject><ispartof>Differential equations, 2019-03, Vol.55 (3), p.303-312</ispartof><rights>Pleiades Publishing, Ltd. 2019</rights><rights>COPYRIGHT 2019 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c279t-8fc97a2525c62a2689b25e192965b0d8c2e3c2eddf4b971306d59fc24aa17a753</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266119030030$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266119030030$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Borukhov, V. T.</creatorcontrib><title>Strong Embeddability of Time-Invariant Nonlinear Differential Systems in Linear Differential Systems</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>We consider a pair (Σ,
w
) consisting of a time-invariant nonlinear differential system Σ and a real piecewise smooth function
w
defined on the state space of the differential system. The notion of strong embeddability of the pair (Σ,
w
) in a linear differential system is introduced. A criterion for the finite-dimensional-strong embeddability of the pair is obtained, linear embedding systems are described, and the explicit representation of first integrals is given for systems in finite-dimensional-strongly embeddable pairs. The class of first integrals determining the general solution of a finite-dimensional-strongly embeddable pair is singled out.</description><subject>Difference and Functional Equations</subject><subject>Embedded systems</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equation</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kM9KAzEQxoMoWKsP4C0vsHWSNMnmWGrVQtFD63nJ5k9J2c1Ksgp9e1PqTZRMGJhvfsPMh9A9gRkhbP6wBSCUCkGIAgYlLtCECKgrBjW7RJOTXJ30a3ST8wEAlCR8gux2TEPc41XfOmt1G7owHvHg8S70rlrHL52CjiN-HWIXotMJPwbvXXJxDLrD22MeXZ9xiHjzt3yLrrzusrv7yVP0_rTaLV-qzdvzernYVIZKNVa1N0pqyik3gmoqatVS7oiiSvAWbG2oY-Vb6-dt2Z6BsFx5Q-daE6klZ1M0O8_d6841IfphTNqUZ10fzBCdD6W-kBSoBFmMmSJyBkwack7ONx8p9DodGwLNydfml6-FoWcml964d6k5DJ8plrv-gb4B7W56Vw</recordid><startdate>20190301</startdate><enddate>20190301</enddate><creator>Borukhov, V. T.</creator><general>Pleiades Publishing</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190301</creationdate><title>Strong Embeddability of Time-Invariant Nonlinear Differential Systems in Linear Differential Systems</title><author>Borukhov, V. T.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c279t-8fc97a2525c62a2689b25e192965b0d8c2e3c2eddf4b971306d59fc24aa17a753</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Difference and Functional Equations</topic><topic>Embedded systems</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Ordinary Differential Equation</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Borukhov, V. T.</creatorcontrib><collection>CrossRef</collection><jtitle>Differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Borukhov, V. T.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Strong Embeddability of Time-Invariant Nonlinear Differential Systems in Linear Differential Systems</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2019-03-01</date><risdate>2019</risdate><volume>55</volume><issue>3</issue><spage>303</spage><epage>312</epage><pages>303-312</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>We consider a pair (Σ,
w
) consisting of a time-invariant nonlinear differential system Σ and a real piecewise smooth function
w
defined on the state space of the differential system. The notion of strong embeddability of the pair (Σ,
w
) in a linear differential system is introduced. A criterion for the finite-dimensional-strong embeddability of the pair is obtained, linear embedding systems are described, and the explicit representation of first integrals is given for systems in finite-dimensional-strongly embeddable pairs. The class of first integrals determining the general solution of a finite-dimensional-strongly embeddable pair is singled out.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0012266119030030</doi><tpages>10</tpages></addata></record> |
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| identifier | ISSN: 0012-2661 |
| ispartof | Differential equations, 2019-03, Vol.55 (3), p.303-312 |
| issn | 0012-2661 1608-3083 |
| language | eng |
| recordid | cdi_gale_infotracacademiconefile_A720270708 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Difference and Functional Equations Embedded systems Mathematics Mathematics and Statistics Ordinary Differential Equation Ordinary Differential Equations Partial Differential Equations |
| title | Strong Embeddability of Time-Invariant Nonlinear Differential Systems in Linear Differential Systems |
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