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  <doc>
    <id>1178</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation>Univ. de Montréal; Univ. de Utrecht; Ivanovo State Power Univ.; Brock Univ. St. Catherines and ZIB Fellow</contributingCorporation>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2010-07-07</completedDate>
    <publishedDate>2010-07-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">N=2 supersymmetric a=4-KdV hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation</title>
    <abstract language="eng">We consider the problem of constructing Gardner's deformations for the $N{=}2$ supersymmetric $a{=}4$--\/Korteweg\/--\/de Vries equation; such deformations yield recurrence relations between the super\/-\/Hamiltonians of the hierarchy. We prove the non\/-\/existence %P.~Mathieu's Open problem on constructing for of supersymmetry\/-\/invariant %Gardner's deformations that %solutions, retract to Gardner's formulas for the KdV equation %whenever it is assumed that, under the %respective component reduction. % in the $N{=}2$ super\/-\/field. the solutions . At the same time, we propose a two\/-\/step scheme for the recursive production of the integrals of motion for the $N{=}2$,\ $a{=}4$--\/SKdV. First, we find a new Gardner's deformation of the Kaup\/--\/Boussinesq equation, which is contained in the bosonic limit of the super\/-\/%$N{=}2$,\ $a{=}4$--\/SKdV hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super\/- /Hamiltonians of the full $N{=}2$, $a{=}4$--\/SKdV hierarchy.</abstract>
    <identifier type="serial">10-16</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1239</identifier>
    <identifier type="doi">10.1063/1.3447731</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11787</identifier>
    <enrichment key="SourceTitle">Appeared under the title "N=2 Supersymmetric a=4 - Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Bousinesq equation" in: J. Math. Phys. 51, 083507 (2010), 19 pages</enrichment>
    <author>V. Hussin</author>
    <submitter>unknown unknown</submitter>
    <author>A. V. Kiselev</author>
    <author>A.O. Krutov</author>
    <author>Thomas Wolf</author>
    <series>
      <title>ZIB-Report</title>
      <number>10-16</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Korteweg-de Vries equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Kaup-Boussinesq equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>supersymmetry</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gardner's deformations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bi-Hamilltonian hierarchies</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="pacs" number="11.30.Pb">Supersymmetry (see also 12.60.Jv Supersymmetric models)</collection>
    <collection role="pacs" number="12.60.Jv">Supersymmetric models (see also 04.65.+e Supergravity)</collection>
    <collection role="msc" number="35Q53">KdV-like equations (Korteweg-de Vries) [See also 37K10]</collection>
    <collection role="msc" number="37K10">Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)</collection>
    <collection role="msc" number="81T60">Supersymmetric field theories</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1178/ZR_10_16.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1178/ZR_10_16.ps</file>
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