Long-time asymptotic analysis of the Korteweg–de Vries equation via the dbar steepest descent method: the soliton region*Dedicated to Dora, Paolo and Sanja, with deep gratitude for their love and support. (7th February 2017)

• Record Type: Journal Article
• Authors: Giavedoni, Pietro
• Is Part Of: Nonlinearity. Volume 30:Number 3(2017:Mar.)
• Page Start: 1165
• Page End: 1181
• Publication Date: 2017-02-07
• Subjects: Riemann–Hilbert problems -- dbar steepest-descent method -- korteweg–de Vries equation -- asymptotic analysis; 35Q53; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa5834
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We address the problem of long-time asymptotics for the solutions of the Korteweg–de Vries equation under low regularity assumptions. We consider decaying initial data admitting only a finite number of moments. For the so-called 'soliton region', an improved asymptotic estimate is provided, in comparison with the one in Grunert and Teschl (2009 Math. Phys. Anal. Geom .12 287–324). Our analysis is based on the dbar steepest descent method proposed by Miller and McLaughlin.