Eur. Phys. J. B (2013) 86: 199
https://doi.org/10.1140/epjb/e2013-31092-6

Regular Article

Modulational instability of Bose-Einstein condensate in a complex polynomial in elliptic Jacobian functions potential

¹ National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
² Département d’informatique et d’ingénierie, Université du Québec en Outaouais, 101 St-Jean-Bosco, Succursale Hull, Gatineau ( PQ ) J8Y 3G5, Canada
³ Department of Mathematics and Statistics, Faculty of Science, University of Ottawa, 585 King Edward Ave., Ottawa, ON K1N 6N5, Canada

^a e-mail: ekengne6@yahoo.fr; kengem01@uqo.ca Emmanuel Kengne dedicates this valuable work to the memory of his Father, papa MTOPI FRANCOIS [TAPEKIOU].

Received: 5 December 2012
Received in final form: 30 January 2013
Published online: 2 May 2013

Abstract

We consider a Gross-Pitaevskii (GP) equation with cubic-quintic nonlinearities, which governs the dynamics of Bose-Einstein condensates (BECs) matter waves with time-dependent complex potential in Jacobian elliptic functions. The complex term of the potential accounts for either the atomic feeding or the atomic loss of the condensate. Based on a special variable transformation, an integrable condition is obtained and used, firstly, to explicitly express the growth rate of a purely growing modulational instability and, secondly, to derive classes of exact solitonic and periodic solutions. Analytical solitonic solutions describe the propagation of both dark and bright solitary waves of the BECs.