Towards the theory of integrable hyperbolic equations of third order

Abstract

The examples are considered of integrable hyperbolic equations of third order with two independent variables. In particular, an equation is found which admits as evolutionary symmetries the Krichever--Novikov equation and the modified Landau--Lifshitz system. The problem of choice of dynamical variables for the hyperbolic equations is discussed.

arXiv comment22 p

References in corpus (3)

• Bäcklund transformation for the Krichever-Novikov equation
• The Camassa-Holm Equation: A Loop Group Approach
• Dressing chain for the acoustic spectral problem

Cited by in corpus (7)

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• Negative flows for several integrable models
• Unfamiliar Aspects of Bäcklund Transformations and an Associated Degasperis-Procesi Equation
• 3D-consistency of negative flows
• On steady motions of an ideal fibre-reinforced fluid in a curved stratum. Geometry and integrability
• On consistent systems of difference equations
• Symmetry structure of integrable hyperbolic third order equations