Symbolic-computation study of bright solitons in the optical waveguides and Bose-Einstein condensates

Abstract

We investigate solitons in optical waveguides and Bose–Einstein condensates (BECs) governed by a (3+1)-dimensional Gross–Pitaevskii system, which describes the propagation of electromagnetic waves in the optical waveguides and ground-state wave functions of the BECs. We use the symbolic computation and Hirota method to derive analytic bright one- and two-soliton solutions under certain conditions. Soliton amplitude/width amplification and the influence of time-modulated dispersion on the bright-soliton shape are studied via graphic analysis. Through the analysis of bright solitons in optical waveguides and BECs, we find that both the amplitude and the width of bright solitons can become larger during propagation with certain choices of time-modulated dispersion, and that the shape of the bright soliton can also be affected by the time-modulated dispersion; when the time-modulated dispersion is different, we can obtain bright parabolic-like and periodic-type solitons.