Letters in Mathematical Physics

, Volume 104, Issue 3, pp 341–360 | Cite as

Vector Hyperbolic Equations on the Sphere Possessing Integrable Third-Order Symmetries



The complete lists of vector hyperbolic equations on the sphere that have integrable third-order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability, we mean the existence of vector Bäcklund transformations depending on a parameter. For all new equations, such transformations are constructed.

Mathematics Subject Classification (2010)

37K10 37K35 35Q53 


higher symmetry exact integrability hyperbolic equation 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Orel State UniversityOrelRussia
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia

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