N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation
- 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)
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.
- OSTI ID:
- 21476544
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 8; Other Information: DOI: 10.1063/1.3447731; (c) 2010 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
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