Cauchy problem of Schrِdinger-Improved Boussinesq Systems on the torus

In this paper, we will study the local well-posedness of Schrödinger-Improved Boussinesq System with additive noise in T d , d ⩾ 1 , and we will also study the global well-posedness of dimension 1 case with the initial data ( u 0 , v 1 , v 2 ) ∈ L 2 × L 2 × L 2 almost surely, gaining some exponential growth of L 2 norm of v.