A new class of exact solitary wave solutions of one dimensional Gross-Pitaevskii equation
arXiv:cond-mat/0512169 · doi:10.1103/PhysRevE.73.056611
Abstract
We present a large family of {\it{exact}} 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 {\it{linear}} 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 {\it{et al.,}} [Nature {\bf{417}{150}{2002}], spatio-temporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates and analytical expression of two-soliton bound states, to name a few.
4 pages, 4 eps figures
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