Type: Article

Modified scattering for the fractional mKdV equation

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

We study the large-time asymptotics of solutions to the fractional modified Korteweg–de Vries equation (0.1) where is the fractional derivative. The case of corresponds to the classical modified KdV equation. In the case of , it is the modified Benjamin–Ono equation. Our aim is to extend the results in [10, 16] for to . We develop the method based on the factorization techniques, which was started in [11], and apply the known results on the - boundedness of pseudodifferential operators to get the large-time asymptotics of solutions.