Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters
We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the 6 N -dimensional phase space Ω of the relativistic systems with 2 N particles and N...
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| Veröffentlicht in: | Journal of mathematical physics 2009-04, Vol.50 (4), p.043511-043511-31 |
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| container_end_page | 043511-31 |
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| container_issue | 4 |
| container_start_page | 043511 |
| container_title | Journal of mathematical physics |
| container_volume | 50 |
| creator | Nimmo, J. J. C. Ruijsenaars, S. N. M. |
| description | We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the
6
N
-dimensional phase space
Ω
of the relativistic systems with
2
N
particles and
N
antiparticles, there exists a
2
N
-dimensional Poincaré-invariant submanifold
Ω
P
corresponding to
N
free particles and
N
bound particle-antiparticle pairs in their ground state. The Tzitzeica
N
-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of
Ω
P
. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state. |
| doi_str_mv | 10.1063/1.3110012 |
| format | Article |
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6
N
-dimensional phase space
Ω
of the relativistic systems with
2
N
particles and
N
antiparticles, there exists a
2
N
-dimensional Poincaré-invariant submanifold
Ω
P
corresponding to
N
free particles and
N
bound particle-antiparticle pairs in their ground state. The Tzitzeica
N
-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of
Ω
P
. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.3110012</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>Exact sciences and technology ; Mathematical methods in physics ; Mathematical models ; Mathematics ; Matrix ; Particle physics ; Physics ; Quantum physics ; Sciences and techniques of general use ; Topological manifolds</subject><ispartof>Journal of mathematical physics, 2009-04, Vol.50 (4), p.043511-043511-31</ispartof><rights>American Institute of Physics</rights><rights>2009 American Institute of Physics</rights><rights>2009 INIST-CNRS</rights><rights>Copyright American Institute of Physics Apr 2009</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c512t-7437badc4edc0a25ab4bd0c3da4dad227801b4a014f8e722174a86ca27a05f7d3</citedby><cites>FETCH-LOGICAL-c512t-7437badc4edc0a25ab4bd0c3da4dad227801b4a014f8e722174a86ca27a05f7d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.3110012$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,794,1558,4509,27922,27923,76154,76160</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21452225$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Nimmo, J. J. C.</creatorcontrib><creatorcontrib>Ruijsenaars, S. N. M.</creatorcontrib><title>Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters</title><title>Journal of mathematical physics</title><description>We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the
6
N
-dimensional phase space
Ω
of the relativistic systems with
2
N
particles and
N
antiparticles, there exists a
2
N
-dimensional Poincaré-invariant submanifold
Ω
P
corresponding to
N
free particles and
N
bound particle-antiparticle pairs in their ground state. The Tzitzeica
N
-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of
Ω
P
. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state.</description><subject>Exact sciences and technology</subject><subject>Mathematical methods in physics</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Matrix</subject><subject>Particle physics</subject><subject>Physics</subject><subject>Quantum physics</subject><subject>Sciences and techniques of general use</subject><subject>Topological manifolds</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNqNkM1KAzEURoMoWKsL32AQXChMzc1kfroRpPiHFTd1He4kGU0Zm5pkBtqV7-Ab-iROadWV4upuzncuHEIOgQ6AZskZDBIASoFtkR7QYhjnWVpskx6ljMWMF8Uu2fN-2hFQcN4jd5OlCUttJEbe1ibYmY9a7XzjI6drDKY1PhgZjbC2T9rZj7f3e-u1i8Kz0zourVpEsm586Db7ZKfC2uuDze2Tx6vLyegmHj9c344uxrFMgYU450leopJcK0mRpVjyUlGZKOQKFWN5QaHkSIFXhc4Zg5xjkUlkOdK0ylXSJ0dr79zZ10b7IKa2cbPupWCQZpDxYdpBJ2tIOuu905WYO_OCbiGAilUqAWKTqmOPN0L0EuvK4Uwa_z1gwFPG2Mp5vua8NKFrY2e_S7-7iq-uou0Ep_8W_AW31v2AYq6q5BNEbJu_</recordid><startdate>20090401</startdate><enddate>20090401</enddate><creator>Nimmo, J. J. C.</creator><creator>Ruijsenaars, S. N. M.</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope></search><sort><creationdate>20090401</creationdate><title>Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters</title><author>Nimmo, J. J. C. ; Ruijsenaars, S. N. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c512t-7437badc4edc0a25ab4bd0c3da4dad227801b4a014f8e722174a86ca27a05f7d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Exact sciences and technology</topic><topic>Mathematical methods in physics</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Matrix</topic><topic>Particle physics</topic><topic>Physics</topic><topic>Quantum physics</topic><topic>Sciences and techniques of general use</topic><topic>Topological manifolds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nimmo, J. J. C.</creatorcontrib><creatorcontrib>Ruijsenaars, S. N. M.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nimmo, J. J. C.</au><au>Ruijsenaars, S. N. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters</atitle><jtitle>Journal of mathematical physics</jtitle><date>2009-04-01</date><risdate>2009</risdate><volume>50</volume><issue>4</issue><spage>043511</spage><epage>043511-31</epage><pages>043511-043511-31</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the
6
N
-dimensional phase space
Ω
of the relativistic systems with
2
N
particles and
N
antiparticles, there exists a
2
N
-dimensional Poincaré-invariant submanifold
Ω
P
corresponding to
N
free particles and
N
bound particle-antiparticle pairs in their ground state. The Tzitzeica
N
-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of
Ω
P
. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.3110012</doi><tpages>31</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of mathematical physics, 2009-04, Vol.50 (4), p.043511-043511-31 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_crossref_primary_10_1063_1_3110012 |
| source | AIP Journals Complete; AIP Digital Archive |
| subjects | Exact sciences and technology Mathematical methods in physics Mathematical models Mathematics Matrix Particle physics Physics Quantum physics Sciences and techniques of general use Topological manifolds |
| title | Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters |
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