The defocusing nonlinear Schrödinger equation with a nonzero background: Painlevé asymptotics in two transition regions
DOI10.1007/s00220-023-04787-6zbMath1529.35483OpenAlexW4382657115MaRDI QIDQ6135937
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
inverse scattering transformRiemann-Hilbert problemnonlinear Schrödinger equationPainlevé II equation
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)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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
This page was built for publication: The defocusing nonlinear Schrödinger equation with a nonzero background: Painlevé asymptotics in two transition regions
