New performances to the perturbed rotation dynamics of the two-dimensional homogeneous Bose–Einstein condensates

Abstract The soliton solutions of the two-dimensional homogeneous Bose–Einstein Condensates Model that is related to the atomic interactions strength and the initial momentum have been discussed through this article to explain the vision when the initial momentum is sufficiently high; the thickness of the bubble-shaped BEC undergoes a counterintuitive thinning. In quantum statistics, the suggested model indicates to two available ways in which a group of noninteracting similar particles may occupy a collection of obtainable possible discrete energy states at thermodynamic equilibrium has been investigated. Many new types of soliton solutions that weren’t achieved before can be constructed, and its descriptions have been documented in the conclusion. In order to derive these new soliton perceptions of the perturbed dynamics of rotating as well as the norm square of the obtaining solution that physically denote to the envelop of these dynamics, we will apply five various schemas. The five distinct schemas that are implemented for the first time to this target are the generalized Kudryashov Schema, the Paul-Painleve Approach schema, the (G′/G)-Expansion Schema, the Extended Simple Equation Schema, and the Riccati–Bernoulli Sub Order Schema are implemented individually, independently in consecutive stages. The consistency for all explored analytical solutions are cleared although these schemas have different tools in prepared. The 2-kind and 3-kind graphs simulations as well as the norm square, which denote physically to envelop of these dynamics, have been documented. The configurator figures that detect the Dynamics’s behaviors as well as all mathematical treatment have been defined via Mathematica program.