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

Journal Article · Sun Aug 15 04:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3447731· OSTI ID:21476544

Hussin, V ^[1]; Kiselev, A V ^[2]; Krutov, A O ^[3]; Wolf, T ^[4]

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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)

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, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
DEFORMATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
HAMILTONIANS
INTEGRALS
KORTEWEG-DE VRIES EQUATION
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
RECURSION RELATIONS
SUPERSYMMETRY
SYMMETRY