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

Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I (Q4916106)

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scientific article; zbMATH DE number 6155918

Language	Label	Description	Also known as
English	Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I	scientific article; zbMATH DE number 6155918

Statements

scholarly article

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

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zbMATH Open document ID

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10.1002/cpa.21445

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Alexander Tovbis

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Communications on Pure and Applied Mathematics

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publication date

19 April 2013

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full work available at URL

https://arxiv.org/abs/1004.1828

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

one-dimensional focusing nonlinear Schrödinger equation

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semiclassical (zero-dispersion) limit of solutions

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point of gradient catastrophe

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Painlevé equation

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tritronquée solution

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MaRDI profile type

MaRDI publication profile

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Rogue waves, rational solutions, the patterns of their zeros and integral relations

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First colonization of a spectral outpost in random matrix theory

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Universality in the Profile of the Semiclassical Limit Solutions to the Focusing Nonlinear Schrodinger Equation at the First Breaking Curve

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Double scaling limit in the random matrix model: The Riemann-Hilbert approach

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The sine-Gordon equation in the semiclassical limit: critical behavior near a separatrix

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Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach

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Universality of a double scaling limit near singular edge points in random matrix models

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Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory

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A steepest descent method for oscillatory Riemann-Hilbert problems

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The semiclassical modified nonlinear Schrödinger equation II: Asymptotic analysis of the Cauchy problem. The elliptic region for transsonic initial data

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On the modified nonlinear Schrödinger equation in the semiclassical limit: supersonic, subsonic, and transonic behavior

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On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation

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Painlevé I asymptotics for orthogonal polynomials with respect to a varying quartic weight

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The isomonodromy approach to matrix models in 2D quantum gravity

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

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Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II

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Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III

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Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function

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On Boutroux's <i>Tritronquée</i> Solutions of the First Painlevé Equation

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Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154)

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Quasi-linear Stokes phenomenon for the Painlevé first equation

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The small dispersion limit of the Korteweg-de Vries equation. I

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The small dispersion limit of the korteweg-de vries equation. ii

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TheN-soliton of the focusing nonlinear Schrödinger equation forN large

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Poles of integrále tritronquée and anharmonic oscillators. A WKB approach

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On the semiclassical limit of the focusing nonlinear Schrödinger equation

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Poles of tritronquée solution to the Painlevé I equation and cubic anharmonic oscillator

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Erratum to: ``Poles of tritronquée solution to the Painlevé I equation and cubic anharmonic oscillator''

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Water waves, nonlinear Schrödinger equations and their solutions

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

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L2-Sobolev space bijectivity of the scattering and inverse scattering transforms

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mardi Publication:4916106

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