The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity

2015/01/21 by Lenells, Jonatan · 1 citation
#35Q15 #35Q53 #41A60 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1501.05329

Abstract

We prove a nonlinear steepest descent theorem for Riemann-Hilbert problems with Carleson jump contours and jump matrices of low regularity and slow decay. We illustrate the theorem by deriving the long-time asymptotics for the mKdV equation in the similarity sector for initial data with limited decay and regularity.

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