Construction of exact multi-soliton solutions to the modified Gross–Pitaevskii equation and further elastic interactions

Abstract

In this paper, the modified Gross–Pitaevskii equation is investigated, taking into account the effects of higher-order interactions (HOIs) in the context of Bose–Einstein condensates. Starting from the theoretical model, subsequent equations of the Hirota bilinear form are built to extract exact analytical multi-soliton solutions, whose details are provided. Fundamental solitons are deeply investigated with emphasis on the wave amplification/compression efficiency. The findings also show how the HOI parameter, beyond amplifying the fundamental wave, affects spatial delocalization in the repulsive and elastic collisional processes in multi-soliton propagation. In addition, further investigations on the elastic interaction of multi-solitons reveal the phenomenon of memory recombination for solitons, which has been evidenced through various interacting procedures. These results may be used as a guide for the production of soliton trains and signal amplification/compression for potential applications in telecommunication devices.