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

Table 1

Type of equilibria of (7).

Regions of (𝑔,𝛿)	Equilibria	Type
(I): 𝛿=3𝑐𝑔2^2/3,𝑔>0	𝐴1,𝐴2	Center, center
(II): 𝛿=3𝑐𝑔2^2/3,𝑔<0	𝐵1,𝐵2	Saddle, saddle
(III): 𝛿<3𝑐𝑔2^2/3,𝑔>0	𝐶1,𝐶2	Center, center
(IV): 𝛿>3𝑐𝑔2^2/3,𝑔>0	𝐷1,𝐷2	Center, center
(V): 𝛿>3𝑐𝑔2^2/3,𝑔<0	𝐸1,𝐸2	Saddle, center
	𝐸3,𝐸4	Center, saddle
(VI): 𝛿<3𝑐𝑔2^2/3,𝑔<0	None	None