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New integrable (\(3+1\))-dimensional systems and contact geometry

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Abstract

We introduce a novel systematic construction for integrable (\(3+1\))-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In particular, we present new large classes of (\(3+1\))-dimensional integrable dispersionless systems associated with the Lax pairs which are polynomial and rational in the spectral parameter.

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Acknowledgements

The author is pleased to thank M. Błaszak, I.S. Krasil’shchik, M. Kunzinger, S. Leble, B. McKay, O.I. Morozov, P.J. Olver, R.O. Popovych, V. Rubtsov, I.A.B. Strachan, L. Vitagliano, and R. Vitolo for stimulating discussions and helpful comments, and to the anonymous referees for useful suggestions.

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  1. Mathematical Institute, Silesian University in Opava, Na Rybníčku 1, 74601, Opava, Czech Republic

    A. Sergyeyev

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Correspondence to A. Sergyeyev.

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This research was performed within the framework of and with financial support of the OPVK program under Project CZ.1.07/2.300/20.0002. Support from the Ministry of Education, Youth and Sport of the Czech Republic (MŠMT ČR) under RVO funding for IČ47813059, as well as from the Grant Agency of the Czech Republic (GA ČR) under grant P201/12/G028, is also gratefully acknowledged.

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Sergyeyev, A. New integrable (\(3+1\))-dimensional systems and contact geometry. Lett Math Phys 108, 359–376 (2018). https://doi.org/10.1007/s11005-017-1013-4

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