A $\dbar$-steepest descent method for oscillatory Riemann-Hilbert problems
Exactly Solvable and Integrable Systems
2021-06-14 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We study the asymptotic behavior of Riemann-Hilbert problems (RHP) arising in the AKNS hierarchy of integrable equations. Our analysis is based on the -steepest descent method. We consider RHPs arising from the inverse scattering transform of the AKNS hierarchy with initial data. The analysis will be divided into three regions: fast decay region, oscillating region and self-similarity region (the Painlev\'e region). The resulting formulas can be directly applied to study the long-time asymptotic of the solutions of integrable equations such as NLS, mKdV and their higher-order generalizations.
Cite
@article{arxiv.2011.14205,
title = {A $\dbar$-steepest descent method for oscillatory Riemann-Hilbert problems},
author = {Fudong Wang and Wen-Xiu Ma},
journal= {arXiv preprint arXiv:2011.14205},
year = {2021}
}
Comments
37 pages, 7 figures; updated version (v2);