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N=2 supersymmetric a=4-KdV hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation

Please always quote using this URN: urn:nbn:de:0297-zib-11787
  • 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.

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Metadaten
Author:V. Hussin, A. V. Kiselev, A.O. Krutov, Thomas Wolf
Document Type:ZIB-Report
Tag:Gardner's deformations; Kaup-Boussinesq equation; Korteweg-de Vries equation; bi-Hamilltonian hierarchies; supersymmetry
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q53 KdV-like equations (Korteweg-de Vries) [See also 37K10]
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Kxx Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] / 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
81-XX QUANTUM THEORY / 81Txx Quantum field theory; related classical field theories [See also 70Sxx] / 81T60 Supersymmetric field theories
PACS-Classification:10.00.00 THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS (for experimental methods and instrumentation for elementary-particle physics, see section 29) / 11.00.00 General theory of fields and particles (see also 03.65.-w Quantum mechanics and 03.70.+k Theory of quantized fields) / 11.30.-j Symmetry and conservation laws (see also 02.20.-a Group theory) / 11.30.Pb Supersymmetry (see also 12.60.Jv Supersymmetric models)
10.00.00 THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS (for experimental methods and instrumentation for elementary-particle physics, see section 29) / 12.00.00 Specific theories and interaction models; particle systematics / 12.60.-i Models beyond the standard model; Unified field theories and models, see 12.10.-g / 12.60.Jv Supersymmetric models (see also 04.65.+e Supergravity)
Contributing Corporation:Univ. de Montréal; Univ. de Utrecht; Ivanovo State Power Univ.; Brock Univ. St. Catherines and ZIB Fellow
Date of first Publication:2010/07/07
Series (Serial Number):ZIB-Report (10-16)
ISSN:1438-0064
ZIB-Reportnumber:10-16
Published in: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
DOI:https://doi.org/10.1063/1.3447731
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