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Bell‐Polynomial Approach and Integrability for the Coupled Gross–Pitaevskii Equations in Bose–Einstein Condensates
Author(s) -
Wang YuFeng,
Tian Bo,
Wang Ming
Publication year - 2013
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12003
Subject(s) - bose–einstein condensate , polynomial , transformation (genetics) , mathematical physics , soliton , bell polynomials , symbolic computation , mathematics , bilinear form , conservation law , bilinear interpolation , physics , mathematical analysis , quantum mechanics , nonlinear system , pure mathematics , biochemistry , chemistry , statistics , gene
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.