Bell-Polynomial Approach and Integrability for the Coupled Gross–Pitaevskii Equations in Bose–Einstein Condensates
Article first published online: 6 FEB 2013
© 2013 by the Massachusetts Institute of Technology
Studies in Applied Mathematics
How to Cite
Wang, Y.-F., Tian, B. and Wang, M. (2013), Bell-Polynomial Approach and Integrability for the Coupled Gross–Pitaevskii Equations in Bose–Einstein Condensates. Studies in Applied Mathematics. doi: 10.1111/sapm.12003
- Article first published online: 6 FEB 2013
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.