A Jacobi elliptic function method for nonlinear arrays of vortices

Arrays of vortices are considered for two-dimensional inviscid flows when the functional relationship between the stream function and the vorticity is hyperbolic sine, exponential, sine, and power functions. The Jacobi elliptic function method with symbolic computation is extended to these nonlinear equations for constructing their doubly periodic wave solutions. The different Jacobi function expansions may lead to new Jacobi doubly periodic wave solutions, triangular periodic solutions and soliton solutions. In addition, as an illustrative sample, the properties for the Jacobi doubly periodic wave solutions of the nonlinear equations are shown with some figures.