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It is shown that the generalized Riemann equation is equivalent with themulticomponent generalization of the Hunter - Saxton equation. New matrix andscalar Lax representation is presented for this generalization. New class ofthe conserved densities, which depends explicitly on the time are obtaineddirectly from the Lax operator. The algorithm, which allows us to generate abig class of the non-polynomial conservation laws of the generalized Riemannequation is presented. Due to this new series of conservation laws of theHunter-Saxton equation is obtained.

The matrix Lax representation of the generalized Riemann equations and its conservation Laws