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  <doc>
    <id>1129</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-05-13</completedDate>
    <publishedDate>2009-05-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hyperdeterminants as integrable discrete systems</title>
    <abstract language="eng">We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A.~Cayley in 1845. We prove integrability (understood as $4d$-consistency) of a nonlinear difference equation defined by the $2 \times 2 \times 2$ - hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the $2\times 2\times 2\times 2$ - hyperdeterminant.</abstract>
    <identifier type="serial">09-17</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1178</identifier>
    <identifier type="doi">10.1088/1751-8113/42/45/454023</identifier>
    <identifier type="arxiv">0903.3864</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11292</identifier>
    <enrichment key="SourceTitle">Appeared in: J. Phys. A: Math. Theor., 42 (2009), 454023, 9 pages</enrichment>
    <author>Sergey Tsarev</author>
    <submitter>unknown unknown</submitter>
    <author>Thomas Wolf</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-17</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hyper determinants</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integrable systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>large polynomial systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>computer algebra</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Form</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Reduce</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Singular</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="pacs" number="02.30.Ik">Integrable systems</collection>
    <collection role="pacs" number="02.70.Wz">Symbolic computation (computer algebra)</collection>
    <collection role="msc" number="52-04">Explicit machine computation and programs (not the theory of computation or programming)</collection>
    <collection role="msc" number="52C99">None of the above, but in this section</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1129/ZR_09_17.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1129/ZR_09_17.ps</file>
  </doc>
  <doc>
    <id>4636</id>
    <completedYear/>
    <publishedYear>2009</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>42</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Hyperdeterminants as integrable discrete systems</title>
    <parentTitle language="eng">Journal of Physics A: Mathematical and Theoretical</parentTitle>
    <identifier type="doi">/10.1088/1751-8113/42/45/454023</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-11292</enrichment>
    <author>Sergey Tsarev</author>
    <submitter> Engel</submitter>
    <author>Thomas Wolf</author>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
  </doc>
  <doc>
    <id>1066</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation>DFG Research Unit 565 "Polyhedral Surfaces'' (TU-Berlin)</contributingCorporation>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-03-05</completedDate>
    <publishedDate>2008-03-05</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Classification of 3-dimensional integrable scalar discrete equations</title>
    <abstract language="eng">We classify all integrable 3-dimensional scalar discrete affine linear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. An equation $Q_3=0$ %of such form is called integrable if it may be consistently imposed on all $3$-dimensional elementary faces of the lattice ${\mathbb Z}^4$. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only ontrivial(non-linearizable) integrable equation from this class is the well-known dBKP-system.</abstract>
    <identifier type="serial">08-13</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1096</identifier>
    <identifier type="arxiv">0706.2464</identifier>
    <identifier type="doi">10.1007/s11005-008-0230-2</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10667</identifier>
    <enrichment key="SourceTitle">Appeared in: Letters in Mathematical Physics, Volume 84, Number 1 (2008), pp. 31-39</enrichment>
    <author>Sergey Tsarev</author>
    <submitter>unknown unknown</submitter>
    <author>Thomas Wolf</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-13</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integrable systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete equations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>large polynomial systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>computer algebra</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>REDUCE</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>FORM</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Crack</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="37K10">Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)</collection>
    <collection role="msc" number="52C99">None of the above, but in this section</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1066/ZR_08_13.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1066/ZR08_13.ps</file>
  </doc>
</export-example>
