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Title: N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation

Abstract

We consider the problem of constructing Gardner's deformations for the N=2 supersymmetric a=4-Korteweg-de Vries (SKdV) equation; such deformations yield recurrence relations between the super-Hamiltonians of the hierarchy. We prove the nonexistence of supersymmetry-invariant deformations that retract to Gardner's formulas for the Korteweg-de Vries (KdV) with equation under the component reduction. 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 superhierarchy. 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. Our method is applicable toward the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.

Authors:
 [1];  [2];  [3];  [4]
  1. Departement de Mathematiques et de Statistique, Universite de Montreal, C.P. 6128, succ. Centre-ville, Montreal, Quebec H3C 3J7 (Canada)
  2. Mathematical Institute, University of Utrecht, P.O. Box 80.010, 3508 TA Utrecht (Netherlands)
  3. Department of Higher Mathematics, Ivanovo State Power University, 34 Rabfakovskaya str., Ivanovo 153003 (Russian Federation)
  4. Department of Mathematics, Brock University, 500 Glenridge Avenue, St. Catharines, Ontario L2S 3A1 (Canada)
Publication Date:
OSTI Identifier:
21476544
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 51; Journal Issue: 8; Other Information: DOI: 10.1063/1.3447731; (c) 2010 American Institute of Physics; Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOSONS; DEFORMATION; HAMILTONIANS; INTEGRALS; KORTEWEG-DE VRIES EQUATION; MATHEMATICAL SOLUTIONS; QUANTUM FIELD THEORY; RECURSION RELATIONS; SUPERSYMMETRY; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD THEORIES; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS; SYMMETRY

Citation Formats

Hussin, V, Kiselev, A V, Krutov, A O, and Wolf, T. N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation. United States: N. p., 2010. Web. doi:10.1063/1.3447731.
Hussin, V, Kiselev, A V, Krutov, A O, & Wolf, T. N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation. United States. https://doi.org/10.1063/1.3447731
Hussin, V, Kiselev, A V, Krutov, A O, and Wolf, T. 2010. "N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation". United States. https://doi.org/10.1063/1.3447731.
@article{osti_21476544,
title = {N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation},
author = {Hussin, V and Kiselev, A V and Krutov, A O and Wolf, T},
abstractNote = {We consider the problem of constructing Gardner's deformations for the N=2 supersymmetric a=4-Korteweg-de Vries (SKdV) equation; such deformations yield recurrence relations between the super-Hamiltonians of the hierarchy. We prove the nonexistence of supersymmetry-invariant deformations that retract to Gardner's formulas for the Korteweg-de Vries (KdV) with equation under the component reduction. 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 superhierarchy. 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. Our method is applicable toward the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.},
doi = {10.1063/1.3447731},
url = {https://www.osti.gov/biblio/21476544}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 8,
volume = 51,
place = {United States},
year = {Sun Aug 15 00:00:00 EDT 2010},
month = {Sun Aug 15 00:00:00 EDT 2010}
}