Some Nonlinear Vortex Solutions

Table 5

Limits of 𝑒^𝜓 from Table 4; ^†means 𝑥 and 𝑦 are interchanged.

	𝑎=0	𝑎=1
EE1	𝑏𝛽^2𝑐𝑛^2(𝛽𝑥∣𝑏)+1+𝛽^2(1−2𝑏)3	HE1^†
EE2	−𝛽^2𝑑𝑐^2𝛽(𝛽𝑥∣𝑏)+^2(1+𝑏)+13	HE2^†
EE3	CE2^†	𝑑𝑐^2(𝑦∣𝑎)+1−𝛽^2(1+𝑏)3
	𝑎=0; 𝑦+𝐾𝑎	𝑎=1; 𝑦+𝐾𝑎
EE1	𝑏𝛽^2𝑐𝑛^2(𝛽𝑥∣𝑏)+1+𝛽^2(1−2𝑏)3	𝑏𝛽^2𝑐𝑛^2𝛽(𝛽𝑥∣𝑏)+^2(1−2𝑏)−13
EE2	−𝛽^2𝑑𝑐^2𝛽(𝛽𝑥∣𝑏)+^2(1+𝑏)+13	−𝛽^2𝑑𝑐^2𝛽(𝛽𝑥∣𝑏)+^2(1+𝑏)−13
EE3	CE2^†	HE4^†
	𝑏=0	𝑏=1
EE1	𝑎𝑐𝑛^2(𝑦∣𝑎)+1−2𝑎+𝛼^23	HE1
EE2	CE1	𝑎𝑐𝑛^2(𝑦∣𝑎)+1−2𝑎−𝛼^23
EE3	CE2	𝑑𝑐^2𝛼(𝑦∣𝑎)+^2−1−𝑎3
	𝑏=0; 𝑥+𝐾𝑏	𝑏=1; 𝑥+𝐾𝑏
EE1	𝑎𝑐𝑛^2(𝑦∣𝑎)+1−2𝑎+𝛼^23	𝑎𝑐𝑛^2(𝑦∣𝑎)+1−2𝑎−𝛼^23
EE2	CE1	HE3
EE3	CE2	HE4
	𝑏=𝑎
EE1	𝑎𝑐𝑛^2(𝑦∣𝑎)+𝑎cn^2(𝑥∣𝑎)	∇^2𝜓=−2𝑒^𝜓
EE2	𝑎𝑑𝑐^2(𝑦∣𝑎)−dc^2(𝑥∣𝑎)+𝑎	∇^2𝜓=−2𝑒^𝜓
EE3	𝑑𝑐^2(𝑦∣𝑎)+dc^2(𝑥∣𝑎)−1	∇^2𝜓=2𝑒^𝜓