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

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Abstract

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 equations. This knowledge is used to deform these heavenly type equations into new integrable PDEs of the second-order with large symmetry pseudogroups. We classify the symmetric deformations obtained in this way and discuss self-dual hyper-Hermitian geometry of their solutions, thus encoding integrability via the twistor theory.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, NT-faculty, University of Tromsø, 90-37, Tromsø, Norway

    Boris Kruglikov

  2. Department of Applied Mathematics, AGH University of Science and Technology, 30-059, Krakow, Poland

    Oleg Morozov

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  1. Boris Kruglikov
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  2. Oleg Morozov
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Correspondence to Boris Kruglikov.

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Kruglikov, B., Morozov, O. Integrable Dispersionless PDEs in 4D, Their Symmetry Pseudogroups and Deformations. Lett Math Phys 105, 1703–1723 (2015). https://doi.org/10.1007/s11005-015-0800-z

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  • DOI: https://doi.org/10.1007/s11005-015-0800-z

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