Global well-posedness for the fractional Schrödinger–Boussinesq system

•The system has clear background in laser and plasma physics.•The system include undetermined nonlinear term f(n)f(n), which can be chosen widely.•Available for other fractional dispersive equations with undetermined nonlinear term.•Improved the global well-posedness results obtained by other authors before.

In this paper, we study the fractional Schrödinger–Boussinesq system raised in the laser and plasma physics, where the nonlinear term f(n)f(n) can be chosen as a large kind of functions. We obtain that it is global well-posed in Hs(R)Hs(R) in one dimensional space, when s⩾1s⩾1.