We model a one-dimensional Bose–Einstein condensate with the one-dimensional Gross–Pitaevskii equation (1D GPE) incorporating higher-order interaction effects. Based on the F-expansion method, we analytically solve the 1D GPE, identifying the typical soliton solution under certain experimental settings within the general wave-like solution set, and demonstrating the applicability of the theoretical treatment that is employed.
Wang, Y., Wang, W., & Zhou, S. (2017). Solitons in One-Dimensional Bose Einstein Condensate with Higher-Order Interactions. Communications in Theoretical Physics, 68(5), 623-626. https://doi.org/10.1088/0253-6102/68/5/623