The defocusing nonlinear Schrödinger equation with a nonzero background: Painlevé asymptotics in two transition regions

DOI10.1007/s00220-023-04787-6zbMath1529.35483OpenAlexW4382657115MaRDI QIDQ6135937

Zhaoyu Wang, En-gui Fan

Publication date: 28 August 2023

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-023-04787-6

zbMATH Keywords

inverse scattering transformRiemann-Hilbert problemnonlinear Schrödinger equationPainlevé II equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) NLS equations (nonlinear Schrödinger equations) (35Q55) Volterra integral equations (45D05) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (4)

The partial-rogue ripple solutions of nonlocal Kadomtsev-Petviashvili equation ⋮ A two-component Sasa-Satsuma equation: large-time asymptotics on the line ⋮ On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation ⋮ Long-time asymptotics of the Hunter-Saxton equation on the line

Cites Work

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• On the asymptotic stability of \(N\)-soliton solutions of the defocusing nonlinear Schrödinger equation
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Long time asymptotics of the Camassa-Holm equation on the half-line
• Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent
• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Long-time asymptotics for integrable systems. Higher order theory
• Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation
• Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
• Long time asymptotic behavior of the focusing nonlinear Schrödinger equation
• Soliton resolution for the derivative nonlinear Schrödinger equation
• Long-time asymptotics of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation with finite-density initial data. II: Dark solitons on continua
• On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions
• Defocusing NLS equation with nonzero background: large-time asymptotics in a solitonless region
• Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Soliton resolution for the short-pulse equation
• The focusing NLS equation with step-like oscillating background: scenarios of long-time asymptotics
• Asymptotic stability in the energy space for dark solitons of the Gross-Pitaevskii equation
• Asymptotic stability of the black soliton for the Gross–Pitaevskii equation
• Regularization of a sharp shock by the defocusing nonlinear Schrödinger equation
• Painlevé-Type Asymptotics for the Camassa–Holm Equation
• The Formula steepest descent method and the asymptotic behavior of polynomials orthogonal on the unit circle with fixed and exponentially varying nonanalytic weights
• The Steepest Descent Method for Orthogonal Polynomials on the Real Line with Varying Weights
• Orbital stability of the black soliton for the Gross-Pitaevskii equation
• The collisionless shock region for the long‐time behavior of solutions of the KdV equation
• Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space
• Connection Problem for the Tau-Function of the Sine-Gordon Reduction of Painlevé-III Equation via the Riemann-Hilbert Approach
• Higher Order Airy and Painlevé Asymptotics for the mKdV Hierarchy
• The modified Camassa-Holm equation on a nonzero background: large-time asymptotics for the Cauchy problem
• Airy and Painlevé asymptotics for the mKdV equation
• Dispersive Asymptotics for Linear and Integrable Equations by the ∂ ¯ $$\overline {\partial }$$ Steepest Descent Method

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