Graded Frölicher-Nijenhuis brackets and the theory of recursion operators for super differential equations. (English) Zbl 0841.58032
Lychagin, V. V. (ed.), The interplay between differential geometry and differential equations. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 167(24), 91-129 (1995).
Summary: The theory of the Frölicher-Nijenhuis bracket for \(n\)-graded commutative algebras is developed. On the basis of this theory, deformations and recursion operators are defined, both in local and nonlocal cases. New recursion operators are computed for super versions of KdV, NLS, and Boussinesq equations. These operators are shown to generate new series of symmetries for these equations.
For the entire collection see [Zbl 0824.00020].
For the entire collection see [Zbl 0824.00020].
MSC:
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 58J15 | Relations of PDEs on manifolds with hyperfunctions |
| 58H10 | Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) |
| 58H15 | Deformations of general structures on manifolds |
| 58J72 | Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds |
| 58A50 | Supermanifolds and graded manifolds |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 16W55 | “Super” (or “skew”) structure |
