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Now showing items 1-10 of 12

#### Nonlinear dynamics of semiclassical coherent states in periodic potentials

(Institute of Physics, 2012-05)

We consider nonlinear Schrödinger equations with either local or nonlocal
nonlinearities. In addition, we include periodic potentials as used, for example, in matter
wave experiments in optical lattices. By considering ...

#### Mathematical and computational methods for semiclassical Schrödinger equations

(Cambridge University Press, 2011-05)

We consider time-dependent (linear and nonlinear) Schr¨odinger equations in
a semiclassical scaling. These equations form a canonical class of (nonlinear)
dispersive models whose solutions exhibit high-frequency oscillations. ...

#### Ground State Properties of Graphene In Hartree-Fock Theory

(American Institute of Physics, 2012-09)

We study the Hartree-Fock approximation of graphene in in -
nite volume, with instantaneous Coulomb interactions. First we construct its
translation-invariant ground state and we recover the well-known fact that, due
to ...

#### Optimal Bilinear control of Gross-Pitaevskii Equations

(Society for Industrial and Applied Mathematics, 2013)

A mathematical framework for optimal bilinear control of nonlinear Schrödinger equations of Gross-Pitaevskii type arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier ...

#### Geometric Optics and Instability for NLS and Davey-Stewartson Models

(European Mathematical Society, 2012-06)

We study the interaction of (slowly modulated) high frequency
waves for multi-dimensional nonlinear Schr odinger equations with gauge invariant
power-law nonlinearities and nonlocal perturbations. The model includes
the ...

#### The Wigner-Fokker-Planck Equation: Stationary States and Large Time Behavior

(World Scientific Publishing, 2012-11)

We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation ...

#### On The Dynamics of Bohmian Measures

(Springer Verlag, 2012)

The present work is devoted to the study of dynamical features of
Bohmian measures, recently introduced by the authors. We rigorously prove
that for su ciently smooth wave functions the corresponding Bohmian measure
furnishes ...

#### Semiclassical Wave Packet Dynamics In Schrodinger Equations With Periodic Potentials

(American Institute of Mathematical Sciences, 2012-05)

We consider semiclassically scaled Schr¨odinger equations with an
external potential and a highly oscillatory periodic potential. We construct asymptotic
solutions in the form of semiclassical wave packets. These solutions ...

#### Existence of solitary waves in dipolar quantum gases

(Elsevier, 2011-02-15)

We study a nonlinear Schrodinger equation arising in the mean
eld description of dipolar quantum gases. Under the assumption of su-
ciently strong dipolar interactions, the existence of standing waves, and hence
solitons, ...

#### On the Cauchy Problem for Nonlinear Schrodinger Equations with Rotation

(American Institute of Mathematical Sciences, 2012-03)

We consider the Cauchy problem for (energy-subcritical) nonlinear Schrodinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for ...