Some symmetry classifications of hyperbolic vector evolution equations

Abstract

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations $u_{tx}=f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ are considered. In each class we find all scaling-homogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.

Revision of published version, incorporating errata on geometric aspects of the sigma model interpretations in the case of homogeneous spaces

References in corpus (1)

• On the Differential Geometry of $G{L}_q(1|1)$

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