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.
Highlights
Nonlinear evolution equations (NLEEs) have been studied in diverse areas in physics and applied mathematics such as plasma physics, nonlinear optical fibers, condensed matter etc [1] [2] [3]
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
The investigation of integrability of certain kinds of (NLEEs) by many researchers has generated a great deals of attention over the past years and many methods to analyze the complete integrability of nonlinear evolution equations are developed
Summary
Nonlinear evolution equations (NLEEs) have been studied in diverse areas in physics and applied mathematics such as plasma physics, nonlinear optical fibers, condensed matter etc [1] [2] [3]. Abbagari et al 1412 wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping [4] [5] As it is known, the investigation of integrability of certain kinds of (NLEEs) by many researchers has generated a great deals of attention over the past years and many methods to analyze the complete integrability of nonlinear evolution equations are developed. We plan to investigate the following Gross-Pitaevskii equation in the Bose-Einstein condensate [36] [37] by the covariant prolongation structure theory:. We will employ symbolic computation to study the integrability aspects and relevant soliton structures of Gross-Pitaevskii equation in the Bose-Einstein condensate [36] [37].
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