Graded Frölicher–Nijenhuis brackets and the theory of recursion operators for super differential equations

1995 ◽  
pp. 91-129
Author(s):  
P. H. M. Kersten ◽  
I. S. Krasil′shchik
Keyword(s):  
Differential Equations ◽  
Recursion Operators

A generalization of recursion operators of differential equations

1999 ◽  
Vol 20 (11) ◽  
pp. 1230-1236 ◽  
Author(s):  
Chen Yufu ◽  
Zhang Hongqing
Keyword(s):  
Differential Equations ◽  
Recursion Operators

scholarly journals Recursion operators and non-local symmetries

1994 ◽  
Vol 446 (1926) ◽  
pp. 107-114 ◽  
Keyword(s):  
Differential Equations ◽  
Differential Operators ◽  
Recursion Operators ◽  
Equal Footing ◽  
Symmetries Of Differential Equations ◽  
Non Local ◽  
Local Symmetries ◽  
New Formulation

A new formulation of recursion operators is presented which eliminates diffi­culties associated with integro-differential operators. This interpretation treats recursion operators and their inverses on an equal footing. Efficient techniques for constructing non-local symmetries of differential equations result.

scholarly journals ALGORITHM FOR CONSTRUCTING A LAX PAIR AND A RECURSION OPERATOR FOR INTEGRABLE EQUATIONS

2019 ◽  
Vol 47 (1) ◽  
pp. 123-126
Author(s):  
I.T. Habibullin ◽  
A.R. Khakimova
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Invariant Manifold ◽  
Nonlinear Partial Differential Equations ◽  
Recursion Operators ◽  
Lax Pairs ◽  
Partial Differential ◽  
Differential Constraint ◽  
Integrable Equations ◽  
Particular Solutions

The method of constructing particular solutions to nonlinear partial differential equations based on the notion of differential constraint (or invariant manifold) is well known in the literature, see (Yanenko, 1961; Sidorov et al., 1984). The matter of the method is to add a compatible equation to a given equation and as a rule, the compatible equation is simpler. Such technique allows one to find particular solutions to a studied equation. In works (Pavlova et al., 2017; Habibullin et al., 2017, 2018; Khakimova, 2018; Habibullin et al., 2016, 2017, 2018) there was proposed a scheme for constructing the Lax pairs and recursion operators for integrable partial differential equations based on the use of similar idea. A suitable generalization is to impose a differential constraint not on the equation, but on its linearization. The resulting equation is referred to as a generalized invariant manifold. In works (Pavlova et al., 2017; Habibullin et al., 2017, 2018; Khakimova, 2018; Habibullin et al., 2016, 2017, 2018) it is shown that generalized invariant varieties allow efficient construction of Lax pairs and recursion operators of integrable equations. The research was supported by the RAS Presidium Program «Nonlinear dynamics: fundamental problems and applications».

ON THE INVERSE PROBLEM OF LAGRANGIAN SUPERMECHANICS

1993 ◽  
Vol 08 (20) ◽  
pp. 3565-3576 ◽  
Author(s):  
L. A. IBORT ◽  
G. LANDI ◽  
J. MARÍN-SOLANO ◽  
G. MARMO
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lagrangian Function ◽  
Necessary And Sufficient Conditions ◽  
Recursion Operators ◽  
Second Order Differential Equations ◽  
Necessary And Sufficient

The inverse problem of Lagrangian supermechanics is investigated. A set of necessary and sufficient conditions for a system of second order differential equations in superspace to derive from a (possibly nonregular) super-Lagrangian function are given. The harmonic superoscillator is revisited and a family of even and odd alternative super-Lagrangians are constructed for it. Finally, we comment on the existence of recursion operators.

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