# 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} }

## 45 Citations

Recursion Operators for Multidimensional Integrable PDEs

- Mathematics, Computer Science
- 2017

We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential…

Five-dimensional lax-integrable equation, its reductions and recursion operator

- Mathematics
- 2015

We consider a five-dimensional nonlinear PDE associated to the five-dimensional equation introduced byMartínez Alonso and Shabat. For our equation we find differential coverings with non-removable…

On an integrable multi-dimensionally consistent 2n + 2n-dimensional heavenly-type equation

- MathematicsProceedings of the Royal Society A
- 2019

The ‘universal’ character of this novel equation of vanishing Pfaffian type is demonstrated by retrieving and generalizing to higher dimensions a great variety of well-known integrable equations such as the dispersionless Kadomtsev–Petviashvili and Hirota equations and various avatars of the heavenly equation governing self-dual Einstein spaces.

Integrable (3+1)-dimensional system with an algebraic Lax pair

- Physics, MathematicsAppl. Math. Lett.
- 2019

Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws

- Physics, MathematicsAnnales Henri Poincaré
- 2019

AbstractWe present an infinite hierarchy of nonlocal conservation laws for the Przanowski equation, an integrable second-order PDE locally equivalent to anti-self-dual vacuum Einstein equations with…

Recursion operators in the cotangent covering of the rdDym equation

- MathematicsAnalysis and Mathematical Physics
- 2021

We describe a general method of constructing nonlocal recursion operators for symmetries of PDEs. As an example, the cotangent equation to the 3D rdDym equation uyt = uxuxy − uyuxx for which two…

Dispersionless (3+1)-dimensional integrable hierarchies

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

A multi-dimensional version of the R-matrix approach to the construction of integrable hierarchies of (3+1)-dimensional dispersionless systems of the type recently introduced in Sergyeyev.

Contact Lax pairs and associated (3+1)-dimensional integrable dispersionless systems

- Mathematics, Physics
- 2019

We review the recent approach to the construction of (3+1)-dimensional integrable dispersionless partial differential systems based on their contact Lax pairs and the related $R$-matrix theory for…

Recursion operators and bi-Hamiltonian structure of the general heavenly equation

- Mathematics, Physics
- 2015

Integrable Dispersionless PDEs in 4D, Their Symmetry Pseudogroups and Deformations

- Mathematics
- 2015

We study integrable non-degenerate Monge–Ampère equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining those…

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