Dynamics of Bose-Einstein Condensates: Exact Representation and Topological Classification of Coherent Matter Waves

Figure 1

An example of the number of roots for 𝑓(𝑅) depending on the sign of 3(𝑐𝑔/2)^2/3−𝛿 with 𝑐=1, 𝑔=−1. There are 4 roots for 𝛿>1.8899, 2 roots for the threshold 𝛿=1.8899, and no root for 𝛿<1.8899.