Vector generalization of a system of equations of interacting high-frequency and low-frequency waves

A vector generalization of the system of equations (0.1) first obtained by one of the authors (V.G.M.) is studied. The vector generalization of the system (0.1) is derived from the multicomponent XXZ Heisenberg model. The Hamiltonian structure is discussed. We obtain some exact single-soliton (regular and singular) solutions to the $U(p, q)$ system (0.1) and associated $U(N)$ nonlinear Schrödinger equation and Zakharov system of equations. For the case of $U(2)$ and $U(1.1)$ versions, existence regions of one-soliton solutions in the $(\alpha,\beta)$ plane are found. Finally, we get a generalization of the $U(p, q)$ system (0.1) taking into account the spin-spin interaction and obtain its exact soliton-like solutions. For certain solutions obtained the energy spectrum is calculated.