On a logarithmic Hartree equation

On the Time Dependent Gross Pitaevskii- and Hartree Equation

We are interested in solutions Ψt of the Schrödinger equation of N interacting bosons under the influence of a time dependent external field, where the range and the coupling constant of the interaction scale with N in such a way, that the interaction energy per particle stays more or less constant. Let N0 be the particle number operator with respect to some φ0 ∈ L (R → C). Assume that the rela...

Gaussons: Solitons of the Logarithmic Schrodinqer Equation

Gaussons: Solitons of the logarithmic Schrodinger equation. Iwo Bialynicki-Birula (Institute of Theoretical Physics, Warsaw University, Warsaw, Poland and Department of Physics, University of Pittsburgh, Pittsburgh, U.S.A.); and J erzy Mycielski (Institute of Theoretical Physics, Warsaw University, Warsaw, Poland). Physica Scripta (Sweden) 20,539-544,1979. Properties of the Schrodinger equation...

A Solution of the Nonlinear Logarithmic Diffusion Equation

In this work, we solve the one-dimensional nonlinear logarithmic diffusion equation using a lattice-Boltzmann model and a d1q3 velocity scheme. Besides, the Tanh solitary wave method is used finding several families of solutions.

Stability of the Hartree equation with time-dependent coefficients

The quantum discrete self-trapping equation in the Hartree approximation

We show how the Hartree approximation (HA) can be used to study the quantum discrete self-trapping (QDST) equation, which in turn provides a model for the quantum description of several interesting nonlinear effects such as energy localization, soliton interactions, and chaos. The accuracy of the Hartree approximation is evaluated by comparing results with exact quantum mechanical calculations ...