# The semiclassical limit of focusing NLS for a family of non-analytic initial data

@article{Jenkins2011TheSL, title={The semiclassical limit of focusing NLS for a family of non-analytic initial data}, author={Robert Jenkins and Kenneth D T Mclaughlin}, journal={arXiv: Analysis of PDEs}, year={2011} }

The small dispersion limit of the focusing nonlinear Schro\"odinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales. The non self-adjoint scattering problem and ill-posed limiting Whitham equa- tions associated to focusing NLS make rigorous asymptotic results difficult. Previous studies [KMM03, TVZ04, TVZ06] have focused on special classes of analytic initial data for which the limiting elliptic Whitham…

## 9 Citations

### Semiclassical Limit of Focusing NLS for a Family of Square Barrier Initial Data

- Mathematics
- 2014

The small dispersion limit of the focusing nonlinear Schrödinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales.…

### Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I

- Mathematics
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The semiclassical (zero‐dispersion) limit of solutions $q=q(x,t,\epsilon)$ to the one‐dimensional focusing nonlinear Schrödinger equation (NLS) is studied in a scaling neighborhood D of a point of…

### Regularization of a sharp shock by the defocusing nonlinear Schrödinger equation

- Mathematics
- 2014

The defocusing nonlinear Schrödinger (NLS) equation is studied for a family of step-like initial data with piecewise constant amplitude and phase velocity with a single jump discontinuity at the…

### Asymptotic stability of $N$-solitons in the cubic NLS equation

- Mathematics
- 2016

In this article we consider the Cauchy problem for the cubic focusing nonlinear Schro\-dinger (NLS) equation on the line with initial datum close to a particular $N$-soliton. Using inverse scattering…

### Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter

- Physics
- 2012

Quasiclassical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation the governing equations are given by elliptic system of quasi-linear…

### Riemann–Hilbert problems and the mKdV equation with step initial data: short-time behavior of solutions and the nonlinear Gibbs-type phenomenon

- Mathematics
- 2012

We produce a family of matrix Riemann–Hilbert (RH) problems parametrized by a given scalar function r(k). The jump matrix of the RH problem depends on r(k) and external real parameters x and t. We…

### Quasi‐Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter

- Physics
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Quasi‐classical approximation in the intrinsic description of the vortex filament dynamics is discussed. Within this approximation, the governing equations are given by elliptic system of…

### Orthogonal Polynomials for a Class of Measures with Discrete Rotational Symmetries in the Complex Plane

- Mathematics
- 2015

We obtain the strong asymptotics of polynomials $$p_n(\lambda )$$pn(λ), $$\lambda \in {\mathbb {C}}$$λ∈C, orthogonal with respect to measures in the complex plane of the form $$\begin{aligned} \hbox…

### Orthogonal Polynomials for a Class of Measures with Discrete Rotational Symmetries in the Complex Plane

- Materials ScienceConstructive Approximation
- 2016

We obtain the strong asymptotics of polynomials pn(λ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}…

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