Analyticity of the Cauchy problem for two-component Hunter–Saxton systems

This paper is mainly concerned with the periodic Cauchy problem for a generalized two-component μμ-Hunter–Saxton system with analytic initial data. The analyticity of its solutions is proved in both variables, globally in space and locally in time. The obtained result can be also applied to its special cases—the classical integrable two-component Hunter–Saxton system, the generalized μμ-Hunter–Saxton equation and the classical Hunter–Saxton equation.