WKB analysis of the logarithmic nonlinear Schrödinger equation in an analytic framework
DOI10.1142/S0219199721500826zbMath1506.35209arXiv2011.12198MaRDI QIDQ5043838
Publication date: 6 October 2022
Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2011.12198
analytic functionssemiclassical limitRiemann invariantsWKB analysislogarithmic nonlinear Schrödinger equationCauchy theoryisothermal Euler system
Asymptotic behavior of solutions to PDEs (35B40) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Analyticity in context of PDEs (35A20) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Exponential and trigonometric functions (33B10) Time-dependent Schrödinger equations and Dirac equations (35Q41) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations
- The domain of analyticity of solutions to the three-dimensional Euler equations in a half space
- Logarithmic nonlinearity in theories of quantum gravity: origin of time and observational consequences
- Compressible fluid flow and systems of conservation laws in several space variables
- Propagation de l'analyticité des solutions de systèmes hyperboliques non-linéaires
- Semiclassical limit of the Gross-Pitaevskii equation in an exterior domain
- Geometric optics and boundary layers for nonlinear-Schrödinger equations
- The Cauchy problem for the Gross--Pitaevskii equation
- Coupling conditions for gas networks governed by the isothermal Euler equations
- WKB analysis for nonlinear Schrödinger equations with potential
- Instabilities for supercritical Schrödinger equations in analytic manifolds
- On a regularization of the compressible Euler equations for an isothermal gas
- WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
- Supercritical geometric optics for nonlinear Schrödinger equations
- Global \(H^1\) solvability of the 3D logarithmic Schrödinger equation
- Nonlinear evolution equations and analyticity. I
- The onset of instability in first-order systems
- Universal dynamics for the defocusing logarithmic Schrödinger equation
- Shock formation in solutions to the \(2D\) compressible Euler equations in the presence of non-zero vorticity
- Global entropy solutions in \(L^\infty\) to the Euler equations and Euler-Poisson equations for isothermal fluids with spherical symmetry
- The compressible Euler equations for an isothermal gas with spherical symmetry
- Rough sound waves in \(3D\) compressible Euler flow with vorticity
- The focusing logarithmic Schrödinger equation: analysis of breathers and nonlinear superposition
- Convergence rate in Wasserstein distance and semiclassical limit for the defocusing logarithmic Schrödinger equation
- Schrödinger group on Zhidkov spaces
- Existence of multi-solitons for the focusing logarithmic non-linear Schrödinger equation
- On the analyticity and Gevrey-class regularity up to the boundary for the Euler equations
- Madelung, Gross–Pitaevskii and Korteweg
- On the Analyticity of the Solutions of Analytic Non-Linear Elliptic Systems of Partial Differential Equations: Part I. Analyticity in the Interior
- Stable solutions of the logarithmic Schrödinger equation
- On the radius of analyticity of solutions to the three-dimensional Euler equations
- Sur la solution à support compact de l’equation d’Euler compressible
- Équations d'évolution avec non linéarité logarithmique
- Semiclassical limit of the nonlinear Schrödinger equation in small time
- Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective
- SEMICLASSICAL LIMIT OF THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION
- WKB analysis of generalized derivative nonlinear Schrödinger equations without hyperbolicity
- The hidden null structure of the compressible Euler equations and a prelude to applications
- Blowup for the compressible isothermal Euler equations with non-vacuum initial data
- Some remarks on the radius of spatial analyticity for the Euler equations
- ON THE LOGARITHMIC SCHRÖDINGER EQUATION
- A note on a Korteweg fluid and the hydrodynamic form of the logarithmic Schrödinger equation
- A review of dispersive limits of (non)linear Schrödinger-type equations
- Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory
- On the semiclassical limit of the general modified NLS equation
- Long range scattering and modified wave operators for some Hartree type equations. III: Gevrey spaces and low dimensions
