Perturbation theory for infinite-dimensional integrable systems on the line. A case study

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The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1] (2001, unknown): “See [8, 11] for an introduction, and [15, 19, 21, 27] for the latest developments.”
On the Asymptotic Stability of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}$$\end{document}-Soliton Solutions (2016, background): “2) and the non robustness of this condition in real life, we remark that we expect that it might be possible to extend the analysis to non integrable systems, like in [19], although admittedly this”
Long time behavior of solutions to the mKdV (2014, background): “As in the case of the NLS [7, 13, 19, 30], Theorem 1.1 is also true for short-range perturbations of the form ut + 1 3 uxxx = (σu3 + F(u))x, u(0) = u0, (1.2) where F ∈ C2(R) satis es |F(u)| = O(|u|p), |u| → 0, p > 3, (1.3) with some minor modi cations if p ∈ (3, 72 ).”