On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

143 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities (2009, background): “ i ∇− A(x) 2 u+V(x)u= 1 ε2 (W∗|u|2)u in R3, u(x,0) = u0(x) in R3. We describe in the following what we expect to hold (the question is open even for A= 0, see the discussion by J. Fr¨ohlich et al. in [17]). Given k≥ 1 positive numbers g1,...,gk, if E : H1(R3) → Ris deﬁned as E(u) = 1 2 Z R3 |∇u|2dx−”
SEMICLASSICAL STATES FOR COUPLED SCHRÖDINGER–MAXWELL EQUATIONS: CONCENTRATION AROUND A SPHERE (2005, methodology): “Other way to try to describe the effect of interaction is through Maxwell equations, see [7, 18].”
Asymptotic dynamics of nonlinear Schrödinger equations: Resonance‐dominated and dispersion‐dominated solutions (2002, background): “ics around solitons (such as the Hartree equations [ 4 ], see also [2]).”
Solitary Wave Dynamics in an External Potential (2003, background): “J.F. thanks T.-P. Tsai and H.-T. Yau for very useful discussions and correspondence which led to the results in [16, 17].”
Uniqueness of ground states for pseudorelativistic Hartree equations (2008, background): “As mentioned before, this spectral result is of independent interest, since it proves a key assumption in [ FTY02 , FGJS04, JFGS06, AS07].”