Quasi-periodic solutions to the two-component nonlinear Klein-Gordon equation

Based on solutions of the stationary zero-curvature equation associated with the 3×3 matrix spectral problem, we introduce a trigonal curve related to the two-component nonlinear Klein-Gordon equation. Resorting to the theory of trigonal curves and properties of the three kinds of Abel differentials, we deduce the explicit theta function representations of the Baker-Akhiezer function and two meromorphic functions. The two-component nonlinear Klein-Gordon flows are straightened using the Abel map and the Lagrange interpolation formula under certain conditions. The explicit theta function representations of solutions for the two-component nonlinear Klein-Gordon equation are constructed with the aid of the asymptotic properties and the algebro-geometric characters of the two meromorphic functions.