In this paper, coupled systems
of Korteweg-de Vries type are considered, where u = u(x, t), v = v(x, t) are real-valued functions and where x, t∈R. Here, subscripts connote partial differentiation and
are quadratic polynomials in the variables u and v. Attention is given to the pure initial-value problem in which u(x, t) and v(x, t) are both specified at t = 0, namely,
for x ∈ ℝ. Under suitable conditions on P and Q, global well-posedness of this problem is established for initial data in the L
2-based Sobolev spaces Hs
(ℝ) × Hs
(ℝ) for any s > ‒3/4.