Exploring the Gross-Pitaevskii Model in Bose-Einstein Condensates and Communication Systems: Features of Solitary Waves and Dynamical Analysis

Abstract

The Gross-Pitaevskii Equation (GPE), which belongs to the class of nonlinear Schrödinger equations is recognized for its applications in diverse fields such as Bose-Einstein Condensates and optical fiber. In this study, the dynamic behaviors of various wave solutions to the M-fractional nonlinear Gross-Pitaevskii equation are examined. Intriguing insights into the mechanisms regulating the intricate wave patterns of the model are offered through this investigation. To secure the solutions, including complex, bright, dark, combined, and singular soliton solutions, the Kumar-Malik method, the modified generalized exponential rational function method, and the generalized multivariate exponential rational integral function method are substantially applied. The fractional parametric effects on solitary waves are observed graphically. Moreover, the Galilean transformation is adopted, and bifurcation, sensitivity, chaotic behavior, 2D and 3D phase portraits, Poincaré maps, time series analysis, and sensitivity to multistability under different conditions are explored.