Mathematical analysis for systems of nonlinear dispersive equations

We study systems of the nonlinear dispersive equations in a general domain. For example, we focus on the Zakharov system, the Schrödinger-improved Boussinesq system and the Klein-Gordon-Schrödinger system. We prove the existence and uniqueness of solutions of the above systems by using the energy and the modified energy method. Moreover, we show the vanishing limit for the Schrödinger-improved Boussinesq system.