Author(s)

Souleymanou Abbagari^1,2,3,4, Hamadou Halidou^2,3,4, Thomas B. Bouetou^3,4, Timoleon C. Kofane^2,4

¹Department of Basic Science, Law and Humanities, Institute of Mines and Petroleum Industries, University of Maroua, Maroua, Cameroon.
²Laboratory of Mechanics, Materials and Structures, Department of physics, University of Yaounde I, Yaounde, Cameroon.
³National Advanced School of Engineering, University of Yaounde I, Yaounde, Cameroon.
⁴Centre d’Excellence en Technologies de l’Information et de la Communication (CETIC), University of Yaounde I, Yaounde, Cameroon.

In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.

Gross-Pitaevskii Equation, Covariant Prolongation Structure Theory, Hidden Structural Symmetries, Hirota’s Bilinear Method

Abbagari, S. , Halidou, H. , B. Bouetou, T. and C. Kofane, T. (2017) Covariant Prolongation Structure, Conservation Laws and Soliton Solutions of the Gross-Pitaevskii Equation in the Bose-Einstein Condensate. Journal of Applied Mathematics and Physics, 5, 1411-1423. doi: 10.4236/jamp.2017.57116.