Dynamics of Matter-Wave Solitons in Multi-component Bose-Einstein Condensates

淳一 家田

Emmanuel Kengne, Abdourahman Shehou, Ahmed Lakhssassi

P. G. Kevrekidis

Paulsamy Muruganandam, M. Lakshmanan

This chapter focuses on exploring localized excitations in the variable coefficient nonlinear Schrodinger (NLS) equation and its generalizations. The motivation comes from the fact that the NLS equation and its variants appear in several branches/topics of physics, including nonlinear optics and Bose-Einstein condensates (BECs). The chapter reviews critically the variety of matter wave solitons and their interactions in single- and multi-component Bose-Einstein condensates. It provides a brief overview of the mean Gross- Pitaevskii (GP) equation, derivation of the one-dimensional GP equation, and mapping of the 1D GP equation to the standard NLS equation. The chapter discusses matter wave single and multi bright and dark solitons of Bose– Einstein condensates with varying trap potentials and atomic interactions. It shows various solitons solutions of multi-component BECs described by the two coupled GP equations. In this case, the coupled GP equation has been mapped onto a two coupled NLS equation.

Yajie Yang, Ying Dong

Abstract The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose–Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross–Pitaevskii equation describing the three-component Bose–Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

淳一 家田