Type: Article

Asymptotics of solutions for the fractional modified Korteweg–de Vries equation of order aE (2,3)

Carreño-Bolaños, Rafael; Hayashi, Nakao; Naumkin, Pavel I;

Abstract:

Abstract We continue to study the large time asymptotics of solutions for the fractional modified Korteweg–de Vries equation where is the fractional derivative. This is a sequel to the previous works in which the cases were studied. It is known that the case of corresponds to the classical modified KdV equation. In the case of it is called the modified Benjamin–Ono equation. In the case it is the nonlinear wave equation and the exceptional case. Our aim is to find the large time asymptotic formulas of solutions. Main difference between the previous works and our result is in the order of fractional derivative The order is a critical point which divides the smoothing property and the derivative loss of solutions.