Magnetic solitons in binary mixtures of Bose-Einstein condensates

Solitons, that is stable localized perturbations of a medium, are the topological excitations of nonlinear systems. They can be stable and live for a long time and may have promising applications for telecommunication. The basic one is the Tsuzuki dark soliton, which can be described by an analytical solution of the Gross-Pitaevskii equation (GPE). Ultracold Bose-Einstein condensed (BEC) gases are an important example for the investigation of solitons which can be created by phase and density imprinting. New possibilities arise in mixtures of different hyperspin states of ultra-cold gases, where the so-called magnetic solitons (MS), that is localized magnetized regions, can exist. We will see that these MS permit an analytical description. New peculiar phenomena can take place in the presence of a coherent Rabi coupling between the spin states, where two different type of solitons existso-called 2 and 0 solitons. 2 solitons, unlike the usual Tsuzuki solitons, have at small velocity a positive effective mass and consequently do not undergo the snake instability. Solitary waves can oscillate in BEC gases along elongated traps. The theoretical description of this motion requires the knowledge of the effective soliton mass and the effective number of particles in the soliton. These quantities are calculated.