Compressed and stabilized bright solitons of a derivative Gross–Pitaevskii model

Abstract

We discuss bright soliton compression in Bose–Einstein condensates described by a cubic-quintic derivative Gross–Pitaevskii model which takes into account the delayed nonlinear response of condensates confined in a complex potential. The external potential consists of an attractive parabolic background, a linear potential that may represent the gravitational field, and a complex part (introduced phenomenologically) which characterizes the rate of injection of atoms into the condensate. In our approach, the bright soliton evolution is described analytically by applying the variational approximation. The influences of the soliton width and the rate of injection of atoms are considered because of practical applications. To ensure the validity of the variational approximation, all analytical results are compared with the numerical data obtained with the split-step Fourier algorithm. The roles of the linear potential on the evolution and stabilization of compressed solitons are unveiled.