<p>This paper develops a class of arbitrarily high-order dissipation-preserving methods for solving the generalized Schrödinger-damped Boussinesq equations. By introducing two quadratic auxiliary variables, we first transform the governing equations into an equivalent system which inherits the mass conservation law, the quadratic energy dissipation law as well as the original energy dissipation law. Then we employ symplectic Runge-Kutta methods for temporal discretization coupled with Fourier pseudospectral spatial discretization. The advantages of these methods include: (1) arbitrarily high-order temporal accuracy; (2) spectral accuracy in spatial directions; (3) rigorous preservation of the discrete mass and energy structures as the continuous model. Furthermore, we construct an efficient iterative solver for the nonlinear algebraic systems generated by our discrete schemes. Finally, some numerical results are presented to demonstrate the convergence performance and structure-preserving properties of the proposed methodology.</p>