The one-dimensional Schrödinger-Newton equations

DOI10.1007/s11005-007-0174-yzbMath1161.35499arXiv0707.0346OpenAlexW2039875152MaRDI QIDQ1013594

Philippe Choquard, Joachim Stubbe

Publication date: 20 April 2009

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

Full work available at URL: https://arxiv.org/abs/0707.0346

zbMATH Keywords

nonlinear Schrödinger equationnonlinear eigenvalue problemrearrangement inequalitySchrödinger-Newton equations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10)

Related Items (17)

Minimizers of the planar Schrödinger–Newton equations ⋮ New result for nonlinear Choquard equations: doubly critical case ⋮ Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions ⋮ On the planar Schrödinger-Poisson system ⋮ Thermal effects in gravitational Hartree systems ⋮ On Rayleigh-type formulas for a non-local boundary value problem associated with an integral operator commuting with the Laplacian ⋮ A guide to the Choquard equation ⋮ The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate ⋮ On a logarithmic Hartree equation ⋮ Bound states of the Schrödinger-Newton model in low dimensions ⋮ Existence of solutions for a fractional Choquard-type equation in \(\mathbb{R}\) with critical exponential growth ⋮ Groundstates of the Choquard equations with a sign-changing self-interaction potential ⋮ Decay and scattering in energy space for the solution of weakly coupled Schrödinger-Choquard and Hartree-Fock equations ⋮ 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 ⋮ Existence and Newtonian limit of nonlinear bound states in the Einstein–Dirac system ⋮ On the asymptotically cubic fractional Schrödinger–Poisson system

Cites Work

• On a class of implicit solutions of the continuity and Euler's equations for 1D systems with long range interactions
• On gravity's role in quantum state reduction
• The Choquard equation and related questions
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• A numerical study of the Schr dinger Newton equations
• On some Probabilistic Aspects of Classical Analysis
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