DYNAMICS OF DARK-DARK SOLITONS AND BREATHERS IN THE TWO-COMPONENT NONLINEAR SCHRODINGER EQUATIONS COUPLED TO BOUSSINESQ EQUATION

General higher-order dark-dark solitons and breathers in the two-component nonlinear Schrodinger equations coupled to Boussinesq (2NLS-Boussinesq) equation are derived by the bilinear KP-hierarchy reduction method, and are given in terms of determinants. These dark-dark solitons only show elastic collisions and the two dark-dark solitons can form bound states. In contrast to the dark-dark solitons in 2NLS equation, which only admits a stationary bound state, the two dark-dark solitons in the 2NLS-Boussinesq equation possesses more bound sates. The dynamics of breathers are also investigated, and they become the homoclinic orbits under particular parametric restrictions.