Long-time behavior of solutions to the fifth-order modified KdV-type equation

Abstract

We consider the long-time behavior of solutions to the fifth-order modified KdV-type equation. For the local-in-time well-posedness, we show that regularity conditions where by a tri-linear estimate holds in the Fourier restriction norm spaces, which is an extension of Kwon's result (2008). Using the method of testing by wave packets, we prove the small-data global existence and modified scattering. We derive the leading asymptotic in both the self-similar and oscillatory regions.