Constantly accelerating attractive BEC wave packet realized by interaction engineering. (a) The engineered interaction parameter g₀(t). Panels (b)–(d) show the evolution of BEC density |ψ(x,t)|², mean values of wave packet position ⟨x⟩ and acceleration a, respectively. The initial interaction is Ng(x,t = 0) = −0.3(x + 10), and the initial wave packet is Eq. (13) with x₀ = 0 and σ₀ = 1, the same as that in Fig. 2(b2).