Condensate bright solitons under transverse confinement

The dynamics of Bose-Einstein condensate (BEC) bright solitons made of alkali-metal atoms with negative scattering length and under harmonic confinement in the transverse direction were investigated. The numerical and analytical estimates of the critical strength beyond which the solitons do not exist, were obtained. The dynamics of the soliton train was simulated numerically by using an effective 1D nonpolynomial nonlinear Schrodinger equation.