Some Nonlinear Vortex Solutions

Table 2

Solutions with one Jacobian function and one hyperbolic or circular function; 𝛼=(1−𝑎𝑎)^1/4, 𝑐₁=(4/27)(2𝑎−2𝛼²−1)(2𝑎+𝛼²−1)² and 𝑐₂=(4/27)(2𝑎+2𝛼²−1)(2𝑎−𝛼²−1)².

exp(𝜓)	∇^2𝜓
𝑎𝑐𝑛^2(𝑦∣𝑎)+𝛼^2sech^2𝛼𝑥+1−2𝑎−𝛼^23	𝑐1𝑒^−2𝑥−2𝑒^𝑥	HE1
𝑑𝑐^2(𝑦∣𝑎)−𝛼^2sech^2𝛼𝛼𝑥+^2−1−𝑎3	𝑐1𝑒^−2𝑥+2𝑒^𝑥	HE2
𝑎𝑐𝑛^2(𝑦∣𝑎)−𝛼^2csch^2𝛼𝑥+1−2𝑎−𝛼^23	𝑐1𝑒^−2𝑥−2𝑒^𝑥	HE3
𝑑𝑐^2(𝑦∣𝑎)+𝛼^2csch^2𝛼𝛼𝑥+^2−1−𝑎3	𝑐1𝑒^−2𝑥+2𝑒^𝑥	HE4
𝑎𝑐𝑛^2(𝑦∣𝑎)−𝛼^2sec^2𝛼𝑥+1−2𝑎+𝛼^23	𝑐2𝑒^−2𝑥−2𝑒^𝑥	CE1
dc^2(𝑦∣𝑎)+𝛼^2sec^2𝛼𝛼𝑥−^2+1+𝑎3	𝑐2𝑒^−2𝑥+2𝑒^𝑥	CE2