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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Integrable and superintegrable systems associated with multi-sums of products</title>
<author><name sortKey="Van Der Kamp, Peter H" sort="Van Der Kamp, Peter H" uniqKey="Van Der Kamp P" first="Peter H." last="Van Der Kamp">Peter H. Van Der Kamp</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Kouloukas, Theodoros E" sort="Kouloukas, Theodoros E" uniqKey="Kouloukas T" first="Theodoros E." last="Kouloukas">Theodoros E. Kouloukas</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Quispel, G R W" sort="Quispel, G R W" uniqKey="Quispel G" first="G. R. W." last="Quispel">G. R. W. Quispel</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Tran, Dinh T" sort="Tran, Dinh T" uniqKey="Tran D" first="Dinh T." last="Tran">Dinh T. Tran</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Vanhaecke, Pol" sort="Vanhaecke, Pol" uniqKey="Vanhaecke P" first="Pol" last="Vanhaecke">Pol Vanhaecke</name>
<affiliation><nlm:aff id="af2"><addr-line>Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS</addr-line>
,<institution>Université de Poitiers</institution>
,<addr-line>86962 Futuroscope Chasseneuil Cedex, France</addr-line>
</nlm:aff>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">PMC</idno>
<idno type="pmid">25484607</idno>
<idno type="pmc">4241012</idno>
<idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4241012</idno>
<idno type="RBID">PMC:4241012</idno>
<idno type="doi">10.1098/rspa.2014.0481</idno>
<date when="2014">2014</date>
<idno type="wicri:Area/Pmc/Corpus">001B14</idno>
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<sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Integrable and superintegrable systems associated with multi-sums of products</title>
<author><name sortKey="Van Der Kamp, Peter H" sort="Van Der Kamp, Peter H" uniqKey="Van Der Kamp P" first="Peter H." last="Van Der Kamp">Peter H. Van Der Kamp</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Kouloukas, Theodoros E" sort="Kouloukas, Theodoros E" uniqKey="Kouloukas T" first="Theodoros E." last="Kouloukas">Theodoros E. Kouloukas</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Quispel, G R W" sort="Quispel, G R W" uniqKey="Quispel G" first="G. R. W." last="Quispel">G. R. W. Quispel</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Tran, Dinh T" sort="Tran, Dinh T" uniqKey="Tran D" first="Dinh T." last="Tran">Dinh T. Tran</name>
<affiliation><nlm:aff id="af1"><addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</nlm:aff>
</affiliation>
</author>
<author><name sortKey="Vanhaecke, Pol" sort="Vanhaecke, Pol" uniqKey="Vanhaecke P" first="Pol" last="Vanhaecke">Pol Vanhaecke</name>
<affiliation><nlm:aff id="af2"><addr-line>Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS</addr-line>
,<institution>Université de Poitiers</institution>
,<addr-line>86962 Futuroscope Chasseneuil Cedex, France</addr-line>
</nlm:aff>
</affiliation>
</author>
</analytic>
<series><title level="j">Proceedings. Mathematical, Physical, and Engineering Sciences / The Royal Society</title>
<idno type="ISSN">1364-5021</idno>
<idno type="eISSN">1471-2946</idno>
<imprint><date when="2014">2014</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
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<profileDesc><textClass></textClass>
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</teiHeader>
<front><div type="abstract" xml:lang="en"><p>We construct and study certain Liouville integrable, superintegrable and non-commutative integrable systems, which are associated with multi-sums of products.</p>
</div>
</front>
</TEI>
<pmc article-type="research-article"><pmc-comment>The publisher of this article does not allow downloading of the full text in XML form.</pmc-comment>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Proc Math Phys Eng Sci</journal-id>
<journal-id journal-id-type="iso-abbrev">Proc. Math. Phys. Eng. Sci</journal-id>
<journal-id journal-id-type="publisher-id">RSPA</journal-id>
<journal-id journal-id-type="hwp">royprsa</journal-id>
<journal-title-group><journal-title>Proceedings. Mathematical, Physical, and Engineering Sciences / The Royal Society</journal-title>
</journal-title-group>
<issn pub-type="ppub">1364-5021</issn>
<issn pub-type="epub">1471-2946</issn>
<publisher><publisher-name>The Royal Society Publishing</publisher-name>
</publisher>
</journal-meta>
<article-meta><article-id pub-id-type="pmid">25484607</article-id>
<article-id pub-id-type="pmc">4241012</article-id>
<article-id pub-id-type="doi">10.1098/rspa.2014.0481</article-id>
<article-id pub-id-type="publisher-id">rspa20140481</article-id>
<article-categories><subj-group subj-group-type="hwp-journal-coll"><subject>1008</subject>
<subject>120</subject>
<subject>59</subject>
</subj-group>
<subj-group subj-group-type="heading"><subject>Research Articles</subject>
</subj-group>
</article-categories>
<title-group><article-title>Integrable and superintegrable systems associated with multi-sums of products</article-title>
<alt-title alt-title-type="short">Multi-sums of products and integrability</alt-title>
</title-group>
<contrib-group><contrib contrib-type="author"><name><surname>van der Kamp</surname>
<given-names>Peter H.</given-names>
</name>
<xref ref-type="aff" rid="af1">1</xref>
<xref ref-type="corresp" rid="cor1"></xref>
</contrib>
<contrib contrib-type="author"><name><surname>Kouloukas</surname>
<given-names>Theodoros E.</given-names>
</name>
<xref ref-type="aff" rid="af1">1</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Quispel</surname>
<given-names>G. R. W.</given-names>
</name>
<xref ref-type="aff" rid="af1">1</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Tran</surname>
<given-names>Dinh T.</given-names>
</name>
<xref ref-type="aff" rid="af1">1</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Vanhaecke</surname>
<given-names>Pol</given-names>
</name>
<xref ref-type="aff" rid="af2">2</xref>
</contrib>
</contrib-group>
<aff id="af1"><label>1</label>
<addr-line>Department of Mathematics</addr-line>
,<institution>La Trobe University</institution>
,<addr-line>Bundoora (Melbourne) Victoria 3086, Australia</addr-line>
</aff>
<aff id="af2"><label>2</label>
<addr-line>Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS</addr-line>
,<institution>Université de Poitiers</institution>
,<addr-line>86962 Futuroscope Chasseneuil Cedex, France</addr-line>
</aff>
<author-notes><corresp id="cor1">e-mail: <email>peterhvanderkamp@gmail.com</email>
</corresp>
</author-notes>
<pub-date pub-type="ppub"><day>8</day>
<month>12</month>
<year>2014</year>
</pub-date>
<volume>470</volume>
<issue>2172</issue>
<elocation-id>20140481</elocation-id>
<history><date date-type="received"><day>17</day>
<month>6</month>
<year>2014</year>
</date>
<date date-type="accepted"><day>15</day>
<month>9</month>
<year>2014</year>
</date>
</history>
<permissions><copyright-statement>© 2014 The Author(s) Published by the Royal Society. All rights reserved.</copyright-statement>
<copyright-year>2014</copyright-year>
</permissions>
<self-uri content-type="pdf" xlink:type="simple" xlink:href="rspa20140481.pdf"></self-uri>
<abstract><p>We construct and study certain Liouville integrable, superintegrable and non-commutative integrable systems, which are associated with multi-sums of products.</p>
</abstract>
<kwd-group><kwd>integrable systems</kwd>
<kwd>Lax representation</kwd>
<kwd>Lotka–Volterra system</kwd>
<kwd>superintegrability</kwd>
<kwd>Kahan discretization</kwd>
</kwd-group>
<custom-meta-group><custom-meta><meta-name>cover-date</meta-name>
<meta-value>December 8, 2014</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
</pmc>
</record>
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