Cauchy problem of Schrödinger-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 TdTd, d⩾1d⩾1, and we will also study the global well-posedness of dimension 1 case with the initial data (u0,v1,v2)∈L2×L2×L2(u0,v1,v2)∈L2×L2×L2 almost surely, gaining some exponential growth of L2L2 norm of v.