On semiclassical (zero dispersion limit) solutions of the focusing nonlinear Schrödinger equation

By Alexander Tovbis, Stephanos Venakides, Xin Zhou. 2004

136 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/77c96a67c09425db0fe4197f62d7d3adec42dc42

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Dispersive shock waves and modulation theory (2016, methodology): “Analysis of these semi-classical structures heavily relies on the integrability of the NLS equation and typically involves a Riemann-Hilbert problem formulation of the IST (see [146, 147] and references therein; also the next section for the discussion of various relations between IST and Whitham th”
Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I (2010, methodology): “2) along the lines of the nonlinear steepest descent method [11, 26], which reduce it to an RHP that allows for an approximation by the so-called model RHP.”
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, methodology): “The situation is somewhat better understood in the integrable setting where the inverse scattering transform (IST) gives one much stronger control on the behavior of solutions thanpurely analytic techniques [12,14,16,20,29,41].”
Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability (2015, methodology): “The Deift-Zhou method was first used to compute the long-time asymptotics of the modified KdV equation [34], and was subsequently extended and employed in numerous works, including the study of the long-time asymptotics of the KdV equation [32], of the defocusing NLS equation [35], and of the Toda l”
Long time asymptotic behavior of the focusing nonlinear Schrödinger equation (2016, unknown): “Such potentials have been extensively studied in the semi-classical limit [23,32,6] where the size of the discrete spectrum becomes asymptotically large.”