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Bell-Polynomial Approach and Integrability for the Coupled Gross–Pitaevskii Equations in Bose–Einstein Condensates


Address for correspondence: Bo Tian, State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China; e-mail:


Under investigation in this paper are the coupled Gross–Pitaevskii equations, which describe the dynamics of two-component Bose–Einstein condensates. Infinitely many conservation laws are obtained based on the Lax pair. Via the Hirota method, Bell-polynomial approach and symbolic computation, bilinear forms, Bell-polynomial-typed transformation, and bilinear-typed Bäcklund transformation are also derived. One- and two-soliton-like solutions are expressed explicitly. The gain/loss coefficient G(t) can influence the velocity of the solitonic envelopes. Head-on and overtaking elastic interactions are shown and analyzed. Inelastic interactions between two soliton-like envelopes are presented as well.