Some Nonlinear Vortex Solutions

Table 1

Solutions with only hyperbolic and circular functions.

exp(𝜓)	∇^2𝜓
cosh^2𝑦+𝜀cos^2𝑥−𝜖+12	(1−𝜀^2)𝑒^−2𝜓	HC1
sec^2𝑥−sech^2𝑦	2𝑒^𝜓	HC2
sec^2𝑥+csch^2𝑦	2𝑒^𝜓	HC3
sech^2𝑦+sech^22𝑥−3	−16𝑒27^−2𝜓−2𝑒^𝜓	HH1
sech^2𝑦−csch^22𝑥−3	−16𝑒27^−2𝜓−2𝑒^𝜓	HH2
csch^2𝑦+csch^22𝑥+3	−16𝑒27^−2𝜓+2𝑒^𝜓	HH3
sec^2𝑦+sec^22𝑥−3	16𝑒27^−2𝜓+2𝑒^𝜓	CC1