Letters in Mathematical Physics

, Volume 108, Issue 2, pp 359–376 | Cite as

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

  • A. SergyeyevEmail author


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.


Dispersionless systems (\(3+1\))-Dimensional integrable systems Contact Lax pairs Contact bracket Conservation laws 

Mathematics Subject Classification

37K05 37K10 53D10 



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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Authors and Affiliations

  1. 1.Mathematical InstituteSilesian University in OpavaOpavaCzech Republic

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