TITLE:
Covariant Prolongation Structure, Conservation Laws and Soliton Solutions of the Gross-Pitaevskii Equation in the Bose-Einstein Condensate
AUTHORS:
Souleymanou Abbagari, Hamadou Halidou, Thomas B. Bouetou, Timoleon C. Kofane
KEYWORDS:
Gross-Pitaevskii Equation, Covariant Prolongation Structure Theory, Hidden Structural Symmetries, Hirota’s Bilinear Method
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.7,
July
18,
2017
ABSTRACT: 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.