# Perturbation at blow-up time of self-similar solutions for the modified Korteweg-de Vries equation

@inproceedings{Correia2022PerturbationAB, title={Perturbation at blow-up time of self-similar solutions for the modified Korteweg-de Vries equation}, author={Sim{\~a}o Correia and Raphael Cote}, year={2022} }

We prove a first stability result of self-similar blow-up for the modified KdV equation on the line. More precisely, given a self-similar solution and a sufficiently small regular profile, there is a unique global solution which behaves at t “ 0 as the sum of the self-similar solution and the smooth perturbation.

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