  We present a general form of multi-dark soliton solutions of two-dimensional
multi-component soliton systems. Multi-dark soliton solutions of the
two-dimensional (2D) and one-dimensional (1D) multi-component Yajima-Oikawa
(YO) systems, which are often called the 2D and 1D multi-component long
wave-short wave resonance interaction systems, are studied in detail. Taking
the 2D coupled YO system with two short wave and one long wave components as an
example, we derive the general $N$-dark-dark soliton solution in both the Gram
type and Wronski type determinant forms for the 2D coupled YO system via the KP
hierarchy reduction method. By imposing certain constraint conditions, the
general $N$-dark-dark soliton solution of the 1D coupled YO system is further
obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed
in detail. In contrast with bright-bright soliton collisions, it is shown that
dark-dark soliton collisions are elastic and there is no energy exchange among
solitons in different components. Moreover, the dark-dark soliton bound states
including the stationary and moving ones are discussed. For the stationary
case, the bound states exist up to arbitrary order, whereas, for the moving
case, only the two-soliton bound state is possible under the condition that the
coefficients of nonlinear terms have opposite signs.
