Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation
Date
2006-05-19Author
Atre, Rajneesh
Panigrahi, Prasanta K.
Agarwal, G. S.
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We present a large family of exact solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain or loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map onto a linear Schrodinger 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 et al. [Nature (London) 417, 150 (2002)], spatiotemporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates, and analytical expression of two-soliton bound states, to name a few.
Citation
Atre, R., Panigrahi, P. K., & Agarwal, G. S. (2006). Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation. Physical Review E, 73(5), Article 056611. https://doi.org/10.1103/PhysRevE.73.056611