Long time behavior of solutions to the mKdV. Issue 2 (1st February 2016)

• Record Type: Journal Article
• Authors: Harrop-Griffiths, Benjamin
• Is Part Of: Communications in partial differential equations. Volume 41:Issue 2(2016)
• Page Start: 282
• Page End: 317
• Publication Date: 2016-02-01
• Subjects: Asymptotic completeness -- modified Korteweg-de Vries -- modified scattering; 35Q53; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2015.1114495
• Languages: English
• ISSNs: 0360-5302

Abstract

ABSTRACT: In this paper we consider the long time behavior of solutions to the modified Korteweg-de Vries equation on ℝ. For sufficiently small, smooth, decaying data we prove global existence and derive modified asymptotics without relying on complete integrability. We also consider the asymptotic completeness problem. Our result uses the method of testing by wave packets, developed in the work of Ifrim and Tataru on the 1 d cubic nonlinear Schrödinger and 2 d water wave equations.