Abstract:
In this investigation, we explore the existence and intriguing features of matter-wave
smooth positons in a non-autonomous one-dimensional Bose–Einstein condensate (BEC) system
with attractive interatomic interactions. We focus on the Gross–Pitaevskii (GP) equation/nonlinear
Schrödinger-type equation with time-modulated nonlinearity and trap potential, which govern
nonlinear wave propagation in the BEC. Our approach involves constructing second- and third-order
matter-wave smooth positons using a similarity transformation technique. We also identify the constraints on the time-modulated system parameters that give rise to these nonlinear localized profiles.
This study considers three distinct forms of modulated nonlinearities: (i) kink-like, (ii) localized or
sech-like, and (iii) periodic. By varying the parameters associated with the nonlinearity strengths, we
observe a rich variety of captivating behaviors in the matter-wave smooth positon profiles. These
behaviors include stretching, curving, oscillating, breathing, collapsing, amplification, and suppression. Our comprehensive studies shed light on the intricate density profile of matter-wave smooth
positons in BECs, providing valuable insights into their controllable behavior and characteristics in
the presence of time-modulated nonlinearity and trap potential effects.
