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.
Semiclassical Propagation of Coherent States for the Hartree Equation / Agissilaos, Athanassoulis; Thierry, Paul; Federica, Pezzotti; Pulvirenti, Mario. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - STAMPA. - 12:8(2011), pp. 1613-1634. [10.1007/s00023-011-0115-2]
Semiclassical Propagation of Coherent States for the Hartree Equation
PULVIRENTI, Mario
2011
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
