2005/12/08 by Rajneesh Atre, Prasanta K. Panigrahi, G. S. Agarwal
Physics and Astronomy · #cond-mat.other
paper · pdf · doi:10.1103/physreve.73.056611
published as Phys. Rev. E 73, 056611 (2006) · 4 pages, 4 eps figures
arxiv created 2005/12/08 · arxiv updated 2009/12/01
We present a large family of \itexact solitary wave solutions of the one dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain/loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map on to a \itlinear Schrödinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Strecker \itet al., [Nature \bf4171502002], spatio-temporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates and analytical expression of two-soliton bound states, to name a few.