TITLE:
New Exact Solutions for the Coupled Gross-Pitaevskii Equation
AUTHORS:
Can Xu, Jianping Li, Junliang Lu
KEYWORDS:
The Coupled Gross-Pitaevskii Equations, The Modified Hyperbolic Function Expanding Method, The Traveling Wave Solutions, Partial Differential Equations
JOURNAL NAME:
Applied Mathematics,
Vol.16 No.4,
April
30,
2025
ABSTRACT: The coupled Gross-Pitaevskii equations are the basic model describing the phenomenon of Bose-Einstein condensation. Therefore, the research on the coupled Gross-Pitaevskii equations is very important. One of the main tasks of studying the coupled Gross-Pitaevskii equations is to obtain the exact solutions. In this paper, the study of the exact solutions of the coupled Gross-Pitaevskii equations is mainly based by using the modified polynomial expansion method and the modified traveling wave solution transformation method, assisted by computer software. Firstly, the coupled Gross-Pitaevskii equations are changed into a nonlinear coupled ordinary differential system by a coupled traveling wave solution transformation. Secondly, by using the modified polynomial expansion method, we successfully obtain more new exact elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions for the coupled Gross-Pitaevskii equations. Finally, according to the special parameter values, we show the figures for some of the exact solutions.