Well-posedness and critical index set of the Cauchy problem for the coupled KdV-KdV systems on \(\mathbb{T}\) (Q2676609)

The authors study solvability of a coupled system of two Korteweg-de Vries equations on the one-dimensional torus in the framework of Sobolev spaces. They determine critical indices for the order of those Sobolev spaces that guarantee (analytic) well-posedness of the Cauchy problem. Unlike the problem posed on the real line, here more complicated dependence appear.