Elastic interaction of second-order rogue matter waves for the modified Gross–Pitaevskii equation with time-dependent trapping potential and gain/loss

Abstract

In this work, we are interested in the one-dimensional modified Gross–Pitaevskii equation with the presence of a confining harmonic time-dependent trap and gain/loss atoms. Starting from Hirota bilinear method, we build the one- and two-soliton solutions in the context of trapping Bose–Einstein condensates. From this set, were generated various second-order rogue matter solitary waves including parabolic solitons, line-like solitons, and dromion-like structures. In addition, great emphasis was put on the influence of higher-order interactions over the amplification and stabilization processes of solitons as well as the effects of the gain/loss whose impact beyond amplification is the creation of areas of collapse and revival of solitons during propagation. Finally, we build the multi-soliton solution then making it possible to describe the elastic-type interaction processes of the various types of rogue matter waves obtained. The theoretical results obtained hence enrich the study of non-linear phenomena within Bose–Einstein condensates and more.