Gaussons: Solitons of the Logarithmic Schrödinger Equation

Abstract

Properties of the Schrödinger equation with the logarithmic nonlinearity are briefly described. This equation possesses soliton-like solutions in any number of dimensions, called gaussons for their Gaussian shape. Excited, stationary states of gaussons of various symmetries, in two and three dimensions are found numerically. The motion of gaussons in uniform electric and magnetic fields is studied and explicit solutions describing linear and rotational internal oscillations are found and analyzed.