Some Nonlinear Vortex Solutions

Table 4

Solutions with two Jacobian functions; 𝛾=𝛼𝛽 and 𝜒=(4/27)[𝛾⁶(𝑏−2)(2𝑏−1)(𝑏+1)+(𝑎−2)(2𝑎−1)(𝑎+1)].

exp(𝜓)	∇^2𝜓
𝑎𝑐𝑛^2(𝑦∣𝑎)+𝑏𝛾^2𝑐𝑛^2(𝛾𝑥∣𝑏)+1−2𝑎+𝛾^2(1−2𝑏)3	𝜒𝑒^−2𝜓−2𝑒^𝜓	EE1
𝑎𝑐𝑛^2(𝑦∣𝑎)−𝛾^2𝑑𝑐^2(𝛾𝑥∣𝑏)+1−2𝑎+𝛾^2(1+𝑏)3	𝜒𝑒^−2𝜓−2𝑒^𝜓	EE2
𝑑𝑐^2(𝑦∣𝑎)+𝛾^2𝑑𝑐^2(𝛾𝑥∣𝑏)−1+𝑎+𝛾^2(1+𝑏)3	𝜒𝑒^−2𝜓+2𝑒^𝜓	EE3