General bright–dark soliton solution to (2 + 1)-dimensional multi-component long-wave–short-wave resonance interaction system

In this paper, we derive a general mixed (bright–dark) multi-soliton solution to a two-dimensional (2D) multi-component long-wave–short-wave resonance interaction (LSRI) system, which include multi-component short waves (SWs) and one-component long wave (LW) for all possible combinations of nonlinearity coefficients including positive, negative and mixed types. With the help of the KP hierarchy reduction method, we firstly construct two types of general mixed N-soliton solution (two-bright–one-dark soliton and one-bright–two-dark one for SW components) to the 2D three-component LSRI system in detail. Then by extending the corresponding analysis to the 2D multi-component LSRI system, a general mixed N-soliton solution in Gram determinant form is obtained. The expression of the mixed soliton solution also contains the general all bright and all dark N-soliton solution as special cases. In particular, for the soliton solution which include two-bright–one-dark soliton for SW components in three-component LSRI system, the dynamics analysis shows that solioff excitation and solioff interaction appear in two SW components which possess bright soliton, while V-type solitary and interaction take place in the other SW component and LW one.