## Faculty of Mathematical Sciences (2002)

### BibTeX

@MISC{Kersten02facultyof,

author = {P. H. M. Kersten and A. S. Sorin and P. H. M. Kersten (a and A. S. Sorin (b},

title = {Faculty of Mathematical Sciences},

year = {2002}

}

### OpenURL

### Abstract

www.math.utwente.nl/publications

### Citations

28 |
Symmetries and recursion operators for classical and supersymmetric differential equations
- Krasil’shchik, Kersten
- 2000
(Show Context)
Citation Context ...siderable progress towards their solution arose quite recently. Thus, the puzzle [5, 6], related to the ”nonexistence” of higher fermionic flows of the N =2α = 1 KdV hierarchy, was partly resolved in =-=[7, 8]-=- by explicit constructing a few bosonic and fermionic nonlocal and nonpolynomial flows and Hamiltonains, then their N = 2 superfield structure and origin were uncovered in [9]. A new property, crucial... |

14 |
1992] Some new cohomological invariants for nonlinear differential equations
- Krasil'shchik
(Show Context)
Citation Context ...s their nonpolynomiality. A new approach to a recursion operator treating it as a form–valued vector field which satisfies a generalized symmetry equation related to a given equation was developed in =-=[10, 11]-=-. Using this approach the recursion operator of the bosonic limit of the N=2 α =1 KdV hierarchy was derived in [12], and its structure, underlining relevance of these Hamiltonians in the bosonic limit... |

12 |
A new N = 2 supersymmetric Korteweg-de Vries Equation
- Labelle, Mathieu
- 1991
(Show Context)
Citation Context ...: Completely Integrable Systems;Supersymmetry; Discrete Symmetries; Recursion Operator;Bi-Hamiltonian Structure1 Introduction The N = 2 supersymmetric α = 1 KdV equation was originally introduced in =-=[1]-=- as a Hamiltonian equation with the N = 2 superconformal algebra as a second Hamiltonian structure, and its integrability was conjectured there due to the existence of a few additional nontrivial boso... |

11 |
Towards the construction of N = 2 supersymmetric integrable hierarchies
- Bonora, Krivonos, et al.
- 1996
(Show Context)
Citation Context ...tric Hamiltonian equations with the N = 2 superconformal algebra as a second Hamiltonian structure (the N =2α = −2 andα = 4 KdV equations [3, 1]), but the N =2α = 1 KdV equation is rather exceptional =-=[4]-=-. Despite knowledge of its Lax–pair description, there remains a lot of longstanding, unsolved problems which resolution would be quite important for a deeper understanding and more detailed descripti... |

10 | Krasil’shchik (2002) Complete integrability of the coupled KdV-mKdV system
- Kersten, J
(Show Context)
Citation Context ...ies a generalized symmetry equation related to a given equation was developed in [10, 11]. Using this approach the recursion operator of the bosonic limit of the N=2 α =1 KdV hierarchy was derived in =-=[12]-=-, and its structure, underlining relevance of these Hamiltonians in the bosonic limit, gives a hint towards its supersymmetric generalization. The present Letter addresses the above–mentioned problems... |

9 |
2 superconformal algebra and integrable O(2) fermionic extensions of the Korteweg–de Vries equation
- Laberge, Mathieu, et al.
- 1988
(Show Context)
Citation Context ...V equation there are another two inequivalent N = 2 supersymmetric Hamiltonian equations with the N = 2 superconformal algebra as a second Hamiltonian structure (the N =2α = −2 andα = 4 KdV equations =-=[3, 1]-=-), but the N =2α = 1 KdV equation is rather exceptional [4]. Despite knowledge of its Lax–pair description, there remains a lot of longstanding, unsolved problems which resolution would be quite impor... |

8 |
The Lax formulation of the ‘new
- Popowicz
- 1993
(Show Context)
Citation Context ...tonian structure, and its integrability was conjectured there due to the existence of a few additional nontrivial bosonic Hamiltonians. Then its Lax–pair representation has indeed been constructed in =-=[2]-=-, and it allowed an algoritmic reconstruction of the whole tower of highest commutative bosonic flows and their Hamiltonians belonging to the N = 2 supersymmetric α = 1 KdV hierarchy. Actually, beside... |

6 |
The N=2 supersymmetric unconstrained matrix GNLS hierarchies
- Sorin, Kersten
(Show Context)
Citation Context ...as partly resolved in [7, 8] by explicit constructing a few bosonic and fermionic nonlocal and nonpolynomial flows and Hamiltonains, then their N = 2 superfield structure and origin were uncovered in =-=[9]-=-. A new property, crucial for the existence of these flows and Hamiltonians, making them distinguished compared to all flows and Hamiltonians of other supersymmetric hierarchies constructed before, is... |

5 |
Structure of the Conservation Laws
- Grabowski, Mathieu
- 1995
(Show Context)
Citation Context ...made to construct a tower of its noncommutative bosonic and fermionic, local and nonlocal symmetries and Hamiltonians, bi-Hamiltonian structure as well as recursion operator (see, e.g. discussions in =-=[5, 6]-=- and references therein). Though these rather complicated problems, solved for the case of the N =2α = −2 andα = 4 KdV hierarchies, still wait their complete resolution for the N =2α = 1 KdV hierarchy... |

5 |
Graded differential equations and their deformations: a computational theory for recursion operators
- Krasil’shchik, Kersten
- 1995
(Show Context)
Citation Context ...s their nonpolynomiality. A new approach to a recursion operator treating it as a form–valued vector field which satisfies a generalized symmetry equation related to a given equation was developed in =-=[10, 11]-=-. Using this approach the recursion operator of the bosonic limit of the N=2 α =1 KdV hierarchy was derived in [12], and its structure, underlining relevance of these Hamiltonians in the bosonic limit... |

4 |
Open problems for SuperKdV equations
- Mathieu
(Show Context)
Citation Context ...made to construct a tower of its noncommutative bosonic and fermionic, local and nonlocal symmetries and Hamiltonians, bi-Hamiltonian structure as well as recursion operator (see, e.g. discussions in =-=[5, 6]-=- and references therein). Though these rather complicated problems, solved for the case of the N =2α = −2 andα = 4 KdV hierarchies, still wait their complete resolution for the N =2α = 1 KdV hierarchy... |

4 |
Symmetries and recursions for N = 2 supersymmetric KdV-equation, in Integrable Hierarchies and Modern Physical Theories, Eds
- Kersten
(Show Context)
Citation Context ...siderable progress towards their solution arose quite recently. Thus, the puzzle [5, 6], related to the ”nonexistence” of higher fermionic flows of the N =2α = 1 KdV hierarchy, was partly resolved in =-=[7, 8]-=- by explicit constructing a few bosonic and fermionic nonlocal and nonpolynomial flows and Hamiltonains, then their N = 2 superfield structure and origin were uncovered in [9]. A new property, crucial... |

4 |
Superalgebraic structure of the N=2 supersymmetric α = 1 KdV hierarchy, in preparation. Bogoliubov Laboratory of Theoretical
- Kersten, Sorin
(Show Context)
Citation Context ...des with the Hamiltonian H3 (H1) (10). A discussion of the complete, very rich superalgebraic structure of the N =2α =1KdV hierarchy is out of the scope of the present Letter and will be discussed in =-=[14]-=-. 5 Recursion operator and bi-Hamiltonian structure of the N =2α =1KdV hierarchy Now, the results of preceding sections give us all necessary inputs to construct the recursion operator of the N =2α = ... |

2 |
Deformation and recursion for the N=2 supersymmetric α = 1 KdV hierarchy, in preparation
- Sorin, Kersten
(Show Context)
Citation Context ...on (16) as well, i.e. proving that associated form–valued vector field is in fact a generalized (with respect to its form–valuedness) symmetry of equation (12). We refer the interested reader to ref. =-=[13]-=- for all details of the complete computations of the results of the next sections. 4 An N = 2 superfield integral of the form (13) has four independent superfield components in general. 44 Nonlocal H... |