Local Existence and WKB Approximation of Solutions to Schrödinger–Poisson System in the Two-Dimensional Whole Space

DOI10.1080/03605301003717142zbMath1232.35155arXiv0912.1388OpenAlexW2962775205MaRDI QIDQ3066911

Satoshi Masaki

Publication date: 20 January 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1388

zbMATH Keywords

nonlinear Schrödinger equationWKB approximationsemiclassical analysis

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (7)

Existence and uniqueness of two dimensional Euler-Poisson system and WKB approximation to the nonlinear Schrödinger-Poisson system ⋮ Trudinger–Moser‐type inequality with logarithmic convolution potentials ⋮ Unnamed Item ⋮ Global energy solutions to a stochastic Schrödinger-Poisson system with multiplicative noise in two dimensions ⋮ Concentration phenomena for the Schrödinger-Poisson system in \(\mathbb{R}^2\) ⋮ Central vortex steady states and dynamics of Bose-Einstein condensates interacting with a microwave field ⋮ On a planar Schrödinger–Poisson system involving a non-symmetric potential

Cites Work

• Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators
• Geometric optics and boundary layers for nonlinear-Schrödinger equations
• Semi-classical limit of Schrödinger--Poisson equations in space dimension \(n\geqslant 3\)
• WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
• Supercritical geometric optics for nonlinear Schrödinger equations
• The two-dimensional Wigner-Poisson problem for an electron gas in the charge neutral case
• Semiclassical limit of the nonlinear Schrödinger equation in small time
• Wigner Measure and the Semiclassical Limit of Schrödinger--Poisson Equations
• Convergence of Nonlinear Schrödinger–Poisson Systems to the Compressible Euler Equations
• The limit from the Schrödinger‐Poisson to the Vlasov‐Poisson equations with general data in one dimension
• Asymptotic expansion of the solution to the nonlinear Schrödinger equation with nonlocal interaction

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