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:
-
- Departement de Mathematiques et de Statistique, Universite de Montreal, C.P. 6128, succ. Centre-ville, Montreal, Quebec H3C 3J7 (Canada)
- Mathematical Institute, University of Utrecht, P.O. Box 80.010, 3508 TA Utrecht (Netherlands)
- Department of Higher Mathematics, Ivanovo State Power University, 34 Rabfakovskaya str., Ivanovo 153003 (Russian Federation)
- 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}
}