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 scalinghomogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.