Symmetry-integrability classifications of hyperbolic vector evolution equations

Abstract:
Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, some symmetry-integrability classifications of $O(N)$-invariant
hyperbolic equations $U_{tx} =f(U,U_t,U_x)$ for an $N$-component vector $U(t,x)$ are presented. In each class all scaling-homogeneous equations admitting a higher-symmetry of least possible scaling weight are obtained by computer-algebra computations. Sigma model interpretations of these equations are used to derive
bi-Hamiltonian formulations giving a proof of integrability.