Localized nonlinear dissipative matter waves controlled by quantum fluctuations

The dynamics of matter waves in a trapped Bose–Einstein condensate including three-body losses, atomic feeding and quantum fluctuations is investigated theoretically and numerically. We use a generalized variational approach which allows us to express the influence of the condensate parameters on the time evolution of the amplitude, width and chirp, through a set of differential equations. Emphasis is placed on the strength of quantum fluctuations which deeply modifies the wave dynamics. Direct numerical simulations confirm the analytical results. Importantly, we extend numerical experiments and show that the localized modes split into two or three trains of solitary waves which can be controlled by the quantum fluctuations.