Multi-component Solitons in Atomic Bose-Einstein Condensates

In this talk, we will mention a number of recent developments on multi-component wave patterns in Bose-Einstein
condensates. We will discuss various states in two-component systems including recently observed ones
experimentally such as dark-antidark solitonic ones. Then we will extend consideration to three-component spinor
settings and first discuss their ground state structure, and subsequently super-impose on the same parametric
space the diagram of existence of different excited nonlinear wave states. We will also present further developments
which go beyond the standard spinor model and towards the classical Manakov model. There we will encounter
dark-bright-bright soliton states and explore how their collisional properties follow predictions of polarization shifts
made on the basis of the theory of integrable systems.