A Coupled KdV Equation is One Case of the Four-Reduction of the KP Hierarchy

It is shown that the coupled KdV equation introduced by the present authors is a special case of the four-reduced KP hierarchy which is included in the general theory of τ functions. From the fact it is also shown that the soliton solutions can be derived from those of the KP equation. Moreover, the existence of infinitely many conserved quantities are proved by means of the linear scheme giving the coupled KdV equation.