A simple construction of recursion operators for multidimensional dispersionless integrable systems

@article{Sergyeyev2017ASC,
  title={A simple construction of recursion operators for multidimensional dispersionless integrable systems},
  author={Artur Sergyeyev},
  journal={Journal of Mathematical Analysis and Applications},
  year={2017},
  volume={454},
  pages={468-480}
}
  • Artur Sergyeyev
  • Published 8 January 2015
  • Mathematics, Physics
  • Journal of Mathematical Analysis and Applications
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References

SHOWING 1-10 OF 62 REFERENCES
Recursion operators for dispersionless integrable systems in any dimension
We present a new approach to construction of recursion operators for multidimensional integrable systems which have a Lax-type representation in terms of a pair of commuting vector fields. It is
Dispersionless integrable systems in 3D and Einstein-Weyl geometry
For several classes of second order dispersionless PDEs, we show that the symbols of their formal linearizations define conformal structures which must be Einstein-Weyl in 3D (or self-dual in 4D) if
A hierarchy of integrable partial differential equations in 2+1 dimensions associated with one-parameter families of one-dimensional vector fields
We introduce a hierarchy of integrable partial differential equations in 2+1 dimensions arising from the commutation of one-parameter families of vector fields, and we construct the formal solution
On Linear Degeneracy of Integrable Quasilinear Systems in Higher Dimensions
We investigate (d + 1)-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case d ≥ 3 we formulate a conjecture that any such system with an
A self-dual Yang-Mills hierarchy and its reductions to integrable systems in 1+1 and 2+1 dimensions
The self-dual Yang-Mills equations play a central role in the study of integrable systems. In this paper we develop a formalism for deriving a four dimensional integrable hierarchy of commuting
Self-dual gravity is completely integrable
We discover a multi-Hamiltonian structure of a complex Monge–Ampere equation (CMA) set in a real first-order 2-component form. Therefore, by Magri's theorem this is a completely integrable system in
Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
In this paper we review some results about the theory of integrable dispersionless PDEs arising as commutation condition of pairs of one-parameter families of vector fields, developed by the authors
Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations
We construct infinite hierarchies of nonlocal higher symmetries for the oriented associativity equations using solutions of associated vector and scalar spectral problems. The symmetries in question
Towards classification of -dimensional integrable equations. Integrability conditions I
In this paper we attempt to extend the symmetry approach (well developed in the case of (1 + 1)-dimensional equations) to the (2 + 1)-dimensional case. Presence of nonlocal terms in symmetries and
...
1
2
3
4
5
...