The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity
Exactly Solvable and Integrable Systems
2017-08-08 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1501.05329,
title = {The nonlinear steepest descent method for Riemann-Hilbert problems of low regularity},
author = {Jonatan Lenells},
journal= {arXiv preprint arXiv:1501.05329},
year = {2017}
}
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34 pages