On the relation between decay and regularity of solutions to the modified Korteweg-de Vries equation

This work is devoted to study the relation between the regularity index and the decay for solutions of the modified Korteweg-de Vries equation in weighted Sobolev spaces. We show if a solution belongs to a Sobolev space and has a large polynomial decay, compared to the regularity, then actually it is more regular than initially considered.