On construction of zero-curvature representations for some chiral-type three-field systems

Abstract:
The problem of construction of matrix zero-curvature representations for some chiral-type three field systems is considered. The systems belong to the class described by the Lagrangian L = [1/2] g_ij(u)uⁱ_x u^j_t + f(u), where g_ij is the metric of three-dimensional reducible Riemannian space. The investigation is based on the analysis of evolutionary system u_t = S(u), where S is a higher symmetry.