TY - JOUR
T1 - Semiclassical Propagation of Coherent States for the Hartree Equation
AU - Athanassoulis, Agissilaos
AU - Paul, Thierry
AU - Pezzotti, Federica
AU - Pulvirenti, Mario
N1 - cited By 4
PY - 2011/12
Y1 - 2011/12
N2 - In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in L2 by ε being the Planck constant. Finally we present a full formal asymptotic expansion. © 2011 Springer Basel AG.
AB - In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. The error can be estimated in L2 by ε being the Planck constant. Finally we present a full formal asymptotic expansion. © 2011 Springer Basel AG.
U2 - 10.1007/s00023-011-0115-2
DO - 10.1007/s00023-011-0115-2
M3 - Article
SN - 1424-0661
VL - 12
SP - 1613
EP - 1634
JO - Annales Henri Poincaré
JF - Annales Henri Poincaré
IS - 8
ER -