Well-posedness and orbital stability of traveling waves for the Schrödinger-improved Boussinesq system

Considered here is the Schrödinger-improved Boussinesq system. First we prove local and global well-posedness in the energy space for the periodic initial-value problem. The proof combines a Strichartz-type estimate with the contraction mapping principle. Second we establish the existence and orbital stability of periodic and solitary traveling-wave solutions. The stability results are set out in the context of abstract Hamiltonian systems.