650 research outputs found
Recursion Operators and Nonlocal Symmetries for Integrable rmdKP and rdDym Equations
We find direct and inverse recursion operators for integrable cases of the
rmdKP and rdDym equations. Also, we study actions of these operators on the
contact symmetries and find shadows of nonlocal symmetries of these equations
Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches
In this review article we discuss four recent methods for computing
Maurer-Cartan structure equations of symmetry groups of differential equations.
Examples include solution of the contact equivalence problem for linear
hyperbolic equations and finding a contact transformation between the
generalized Hunter-Saxton equation and the Euler-Poisson equation.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Integrable dispersionless PDE in 4D, their symmetry pseudogroups and deformations
We study integrable non-degenerate Monge-Ampere equations of Hirota type in
4D and demonstrate that their symmetry algebras have a distinguished graded
structure, uniquely determining the equations. This is used to deform these
heavenly type equations into new integrable PDE of the second order with large
symmetry pseudogroups. We classify the obtained symmetric deformations and
discuss self-dual hyper-Hermitian geometry of their solutions, which encode
integrability via the twistor theory.Comment: This version is updated with an appendix about multi-component
extensions of the integrable equations. Our deformations can be considered as
reductions of such extensions (as they are reductions of the self-duality
equation), but we stress that second order deformations carry the natural
geometry which encodes integrability. We also expanded the introduction a bi
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