Well-posedness of the Cauchy problem for the modified KdV equation with periodic boundary condition

By Hideo Takaoka, Y. Tsutsumi. 2004

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On unconditional well-posedness of modified KdV (2010, background): “) As pointed out in [12], if we define v by”
Invariance of the Gibbs measure for the periodic quartic gKdV (2012, methodology): “A similar factorization takes place in the analysis of mKdV (with cubic nonlinearity), and the region A−1 is not included, see for example [31].”
Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces (2018, unknown): “1) is known to be locally well-posed in Hs(M) for s ≥ 1 4 on the real line [32, 55] and for s ≥ 1 3 on the circle [8, 54, 43, 42].”