The hilbert problem for matrices and a new class of integrable equations

A series of new integrable nonlinear differential equations is derived as compatibility conditions between generalized Lax pairs of operators which are meromorphic functions of the spectral parameter on the Riemann surface S of genus 1. On employing the Hilbert problem for the surface S, a general method of integration of these equations is proposed. The method is applied to obtain soliton solutions for asymmetric chiral SU(2) theory.