On the integration of a class of nonlinear systems of ordinary differential equations
For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this pape...
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| creator | Talyshev, Aleksandr A. |
| description | For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition. |
| doi_str_mv | 10.1063/1.5012679 |
| format | Conference Proceeding |
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In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.</description><subject>Complex numbers</subject><subject>Inverse problems</subject><subject>Mathematical analysis</subject><subject>Nonlinear systems</subject><subject>Ordinary differential equations</subject><subject>Partial differential equations</subject><issn>0094-243X</issn><issn>1551-7616</issn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2017</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNp9kEtLAzEUhYMoWKsL_0HAnTA1N6-ZLKVoFQrdWHAXMjOJpkwz0yQV-u_tC9y5upfLd849HITugUyASPYEE0GAylJdoBEIAUUpQV6iESGKF5Szz2t0k9KKEKrKshqh5SLg_G2xD9l-RZN9H3DvsMFNZ1I6rKEPnQ_WRJx2Kdv18djH1gcTd7j1ztloQ_amw3azPTqkW3TlTJfs3XmO0fL15WP6VswXs_fp87wYqGC5aFwrqVBcUFtyzgTUlbGg2ta0lCte1ba2rJGgJBOWADO2qg0oRV0lHYeGjdHDyXeI_WZrU9arfhvD_qWmAJIIVtFyTz2eqNT4fAyoh-jX-_j6p48a9LkyPbTuPxiIPnT8J2C_GVtuTg</recordid><startdate>20171114</startdate><enddate>20171114</enddate><creator>Talyshev, Aleksandr A.</creator><general>American Institute of Physics</general><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20171114</creationdate><title>On the integration of a class of nonlinear systems of ordinary differential equations</title><author>Talyshev, Aleksandr A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p253t-cfd6259452e744351b8ae19ddad24948bebe3c619635e013ae8ba1992f86f41c3</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Complex numbers</topic><topic>Inverse problems</topic><topic>Mathematical analysis</topic><topic>Nonlinear systems</topic><topic>Ordinary differential equations</topic><topic>Partial differential equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Talyshev, Aleksandr A.</creatorcontrib><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Talyshev, Aleksandr A.</au><au>Popov, Sergey V.</au><au>Ivanova, Anna O.</au><au>Egorov, Ivan E.</au><au>Antonov, Mikhail Yu</au><au>Vabishchevich, Petr N.</au><au>Lazarev, Nyurgun P.</au><au>Troeva, Marianna S.</au><au>Grigor’ev, Yuri M.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>On the integration of a class of nonlinear systems of ordinary differential equations</atitle><btitle>AIP conference proceedings</btitle><date>2017-11-14</date><risdate>2017</risdate><volume>1907</volume><issue>1</issue><issn>0094-243X</issn><eissn>1551-7616</eissn><coden>APCPCS</coden><abstract>For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.5012679</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0094-243X |
| ispartof | AIP conference proceedings, 2017, Vol.1907 (1) |
| issn | 0094-243X 1551-7616 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_1_5012679 |
| source | AIP Journals Complete |
| subjects | Complex numbers Inverse problems Mathematical analysis Nonlinear systems Ordinary differential equations Partial differential equations |
| title | On the integration of a class of nonlinear systems of ordinary differential equations |
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