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We present a general form of multi-dark soliton solutions of two-dimensionalmulti-component soliton systems. Multi-dark soliton solutions of thetwo-dimensional (2D) and one-dimensional (1D) multi-component Yajima-Oikawa(YO) systems, which are often called the 2D and 1D multi-component longwave-short wave resonance interaction systems, are studied in detail. Takingthe 2D coupled YO system with two short wave and one long wave components as anexample, we derive the general $N$-dark-dark soliton solution in both the Gramtype and Wronski type determinant forms for the 2D coupled YO system via the KPhierarchy reduction method. By imposing certain constraint conditions, thegeneral $N$-dark-dark soliton solution of the 1D coupled YO system is furtherobtained. The dynamics of one dark-dark and two dark-dark solitons are analyzedin detail. In contrast with bright-bright soliton collisions, it is shown thatdark-dark soliton collisions are elastic and there is no energy exchange amongsolitons in different components. Moreover, the dark-dark soliton bound statesincluding the stationary and moving ones are discussed. For the stationarycase, the bound states exist up to arbitrary order, whereas, for the movingcase, only the two-soliton bound state is possible under the condition that thecoefficients of nonlinear terms have opposite signs.

Multi-dark soliton solutions of the two-dimensional multi-component Yajima-Oikawa systems