A bilinear approach to discrete Miura transformations
Identifieur interne : 002C84 ( Istex/Corpus ); précédent : 002C83; suivant : 002C85A bilinear approach to discrete Miura transformations
Auteurs : N. Joshi ; A. Ramani ; B. GrammaticosSource :
- Physics Letters A [ 0375-9601 ] ; 1998.
English descriptors
- KwdEn :
- Bilinear, Bilinear formalism, Discrete logarithmic derivatives, Discrete painlevc equations, Elsevier science, Fokas, Grammaticos, Homogeneous equation, Joshi, Miura, Miura transformation, Miura transformations, Nonlinear, Nonlinear equation, Phys, Previous case, Ramani, Same equation, Satsuma, Schlesinger, Schlesinger transformations, Singularity, Singularity patterns, Singularity structure.
- Teeft :
- Bilinear, Bilinear formalism, Discrete logarithmic derivatives, Discrete painlevc equations, Elsevier science, Fokas, Grammaticos, Homogeneous equation, Joshi, Miura, Miura transformation, Miura transformations, Nonlinear, Nonlinear equation, Phys, Previous case, Ramani, Same equation, Satsuma, Schlesinger, Schlesinger transformations, Singularity, Singularity patterns, Singularity structure.
Abstract
Abstract: We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of τ-functions. Elimination of τ-functions from the resulting system leads to another nonlinear equation, which is a “modified” version of the original equation. The procedure therefore yields Miura transformations. In this Letter, we illustrate this approach by reproducing previously known Miura transformations and constructing new ones.
Url:
DOI: 10.1016/S0375-9601(98)00624-0
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Joshi</name><affiliation><mods:affiliation>Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia</mods:affiliation></affiliation></author><author><name sortKey="Ramani, A" sort="Ramani, A" uniqKey="Ramani A" first="A." last="Ramani">A. Ramani</name><affiliation><mods:affiliation>CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau, France</mods:affiliation></affiliation></author><author><name sortKey="Grammaticos, B" sort="Grammaticos, B" uniqKey="Grammaticos B" first="B." last="Grammaticos">B. Grammaticos</name><affiliation><mods:affiliation>GMPIB, Université Paris VII, Tour 24-14, 5e étage, 75251 Paris, France</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Physics Letters A</title><title level="j" type="abbrev">PLA</title><idno type="ISSN">0375-9601</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1998">1998</date><biblScope unit="volume">249</biblScope><biblScope unit="issue">1–2</biblScope><biblScope unit="page" from="59">59</biblScope><biblScope unit="page" to="62">62</biblScope></imprint><idno type="ISSN">0375-9601</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0375-9601</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Bilinear</term><term>Bilinear formalism</term><term>Discrete logarithmic derivatives</term><term>Discrete painlevc equations</term><term>Elsevier science</term><term>Fokas</term><term>Grammaticos</term><term>Homogeneous equation</term><term>Joshi</term><term>Miura</term><term>Miura transformation</term><term>Miura transformations</term><term>Nonlinear</term><term>Nonlinear equation</term><term>Phys</term><term>Previous case</term><term>Ramani</term><term>Same equation</term><term>Satsuma</term><term>Schlesinger</term><term>Schlesinger transformations</term><term>Singularity</term><term>Singularity patterns</term><term>Singularity structure</term></keywords><keywords scheme="Teeft" xml:lang="en"><term>Bilinear</term><term>Bilinear formalism</term><term>Discrete logarithmic derivatives</term><term>Discrete painlevc equations</term><term>Elsevier science</term><term>Fokas</term><term>Grammaticos</term><term>Homogeneous equation</term><term>Joshi</term><term>Miura</term><term>Miura transformation</term><term>Miura transformations</term><term>Nonlinear</term><term>Nonlinear equation</term><term>Phys</term><term>Previous case</term><term>Ramani</term><term>Same equation</term><term>Satsuma</term><term>Schlesinger</term><term>Schlesinger transformations</term><term>Singularity</term><term>Singularity patterns</term><term>Singularity structure</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of τ-functions. Elimination of τ-functions from the resulting system leads to another nonlinear equation, which is a “modified” version of the original equation. The procedure therefore yields Miura transformations. In this Letter, we illustrate this approach by reproducing previously known Miura transformations and constructing new ones.</div></front></TEI><istex><corpusName>elsevier</corpusName><keywords><teeft><json:string>miura</json:string><json:string>ramani</json:string><json:string>phys</json:string><json:string>grammaticos</json:string><json:string>miura transformations</json:string><json:string>nonlinear</json:string><json:string>miura transformation</json:string><json:string>schlesinger transformations</json:string><json:string>satsuma</json:string><json:string>fokas</json:string><json:string>joshi</json:string><json:string>singularity</json:string><json:string>singularity structure</json:string><json:string>nonlinear equation</json:string><json:string>bilinear formalism</json:string><json:string>bilinear</json:string><json:string>elsevier science</json:string><json:string>same equation</json:string><json:string>singularity patterns</json:string><json:string>previous case</json:string><json:string>homogeneous equation</json:string><json:string>discrete logarithmic derivatives</json:string><json:string>discrete painlevc equations</json:string><json:string>schlesinger</json:string></teeft></keywords><author><json:item><name>N. Joshi</name><affiliations><json:string>Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia</json:string></affiliations></json:item><json:item><name>A. Ramani</name><affiliations><json:string>CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau, France</json:string></affiliations></json:item><json:item><name>B. Grammaticos</name><affiliations><json:string>GMPIB, Université Paris VII, Tour 24-14, 5e étage, 75251 Paris, France</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Nonlinear science</value></json:item></subject><arkIstex>ark:/67375/6H6-HQ58CL0H-2</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>Full-length article</json:string></originalGenre><abstract>Abstract: We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of τ-functions. Elimination of τ-functions from the resulting system leads to another nonlinear equation, which is a “modified” version of the original equation. The procedure therefore yields Miura transformations. 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Fordy</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">A bilinear approach to discrete Miura transformations</title><author xml:id="author-0000"><persName><forename type="first">N.</forename><surname>Joshi</surname></persName><affiliation>Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia</affiliation></author><author xml:id="author-0001"><persName><forename type="first">A.</forename><surname>Ramani</surname></persName><affiliation>CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau, France</affiliation></author><author xml:id="author-0002"><persName><forename type="first">B.</forename><surname>Grammaticos</surname></persName><affiliation>GMPIB, Université Paris VII, Tour 24-14, 5e étage, 75251 Paris, France</affiliation></author><idno type="istex">ED75A94C95EF3B52EAEA65D2F0757B185CAA0099</idno><idno type="DOI">10.1016/S0375-9601(98)00624-0</idno><idno type="PII">S0375-9601(98)00624-0</idno></analytic><monogr><title level="j">Physics Letters A</title><title level="j" type="abbrev">PLA</title><idno type="pISSN">0375-9601</idno><idno type="PII">S0375-9601(00)X0203-4</idno><imprint><publisher>ELSEVIER</publisher><date type="published" when="1998"></date><biblScope unit="volume">249</biblScope><biblScope unit="issue">1–2</biblScope><biblScope unit="page" from="59">59</biblScope><biblScope unit="page" to="62">62</biblScope></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1998</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of τ-functions. Elimination of τ-functions from the resulting system leads to another nonlinear equation, which is a “modified” version of the original equation. The procedure therefore yields Miura transformations. In this Letter, we illustrate this approach by reproducing previously known Miura transformations and constructing new ones.</p></abstract><textClass><keywords scheme="keyword"><list><head>article-category</head><item><term>Nonlinear science</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1998">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/ED75A94C95EF3B52EAEA65D2F0757B185CAA0099/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Elsevier, elements deleted: tail"><istex:xmlDeclaration>version="1.0" encoding="utf-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//ES//DTD journal article DTD version 4.5.2//EN//XML" URI="art452.dtd" name="istex:docType"></istex:docType><istex:document><converted-article version="4.5.2" docsubtype="fla"><item-info><jid>PLA</jid><aid>98006240</aid><ce:pii>S0375-9601(98)00624-0</ce:pii><ce:doi>10.1016/S0375-9601(98)00624-0</ce:doi><ce:copyright type="unknown" year="1998"></ce:copyright><ce:doctopics><ce:doctopic><ce:text>Nonlinear science</ce:text></ce:doctopic></ce:doctopics></item-info><head><ce:article-footnote><ce:label>☆</ce:label><ce:note-para>The research reported in this Letter was partially supported by the Australian Research Council.</ce:note-para></ce:article-footnote><ce:title>A bilinear approach to discrete Miura transformations</ce:title><ce:author-group><ce:author><ce:given-name>N.</ce:given-name><ce:surname>Joshi</ce:surname><ce:cross-ref refid="AFF1"><ce:sup>a</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>A.</ce:given-name><ce:surname>Ramani</ce:surname><ce:cross-ref refid="AFF2"><ce:sup>b</ce:sup></ce:cross-ref></ce:author><ce:author><ce:given-name>B.</ce:given-name><ce:surname>Grammaticos</ce:surname><ce:cross-ref refid="AFF3"><ce:sup>c</ce:sup></ce:cross-ref></ce:author><ce:affiliation id="AFF1"><ce:label>a</ce:label><ce:textfn>Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia</ce:textfn></ce:affiliation><ce:affiliation id="AFF2"><ce:label>b</ce:label><ce:textfn>CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau, France</ce:textfn></ce:affiliation><ce:affiliation id="AFF3"><ce:label>c</ce:label><ce:textfn>GMPIB, Université Paris VII, Tour 24-14, 5<ce:sup>e</ce:sup> étage, 75251 Paris, France</ce:textfn></ce:affiliation></ce:author-group><ce:date-received day="15" month="4" year="1998"></ce:date-received><ce:date-accepted day="7" month="8" year="1998"></ce:date-accepted><ce:miscellaneous>Communicated by A.P. Fordy</ce:miscellaneous><ce:abstract><ce:section-title>Abstract</ce:section-title><ce:abstract-sec><ce:simple-para>We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the nonlinear discrete equation in terms of τ-functions. Elimination of τ-functions from the resulting system leads to another nonlinear equation, which is a “modified” version of the original equation. The procedure therefore yields Miura transformations. In this Letter, we illustrate this approach by reproducing previously known Miura transformations and constructing new ones.</ce:simple-para></ce:abstract-sec></ce:abstract></head></converted-article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>A bilinear approach to discrete Miura transformations</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A bilinear approach to discrete Miura transformations</title></titleInfo><name type="personal"><namePart type="given">N.</namePart><namePart type="family">Joshi</namePart><affiliation>Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Ramani</namePart><affiliation>CPT, Ecole Polytechnique, CNRS, UPR 14, 91128 Palaiseau, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">B.</namePart><namePart type="family">Grammaticos</namePart><affiliation>GMPIB, Université Paris VII, Tour 24-14, 5e étage, 75251 Paris, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="Full-length article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>ELSEVIER</publisher><dateIssued encoding="w3cdtf">1998</dateIssued><copyrightDate encoding="w3cdtf">1998</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><abstract lang="en">Abstract: We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. 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