Matter-Wave Solitons in Bose-Einstein Condensates

The observation of Bose-Einstein condensates (BEC) in 1995 is one of the greatest achievements of modern physics. It took almost 70 years after the theoretical prediction of BEC by A. Einstein. The BEC is an outcome of B-E statistics which is a generalized version of photon statistics introduced by S.N. Bose while discussing the black-body spectrum. In this book, we have started with the blackbody spectrum and discuss progress toward the observation of the BEC. We have introduced mean-field for the description of the ground state properties of the condensates. The mean-field interaction gives birth to nonlinearity in the BEC and thus leads to the formation of matter-wave soliton. In this book we discuss the dynamics of matter-wave bright solitons in Bose-Einstein condensates in the presence of external potentials, namely, harmonic trap and optical lattices (both linear and nonlinear optical lattices). We introduce a variational approach and Ritz optimization procedure to deal with the soliton problem for both conservative and dissipative systems. A linear stability analysis for matter-wave solitons has been discussed.