Standard forms of elliptic integrals and their applications to nonlinear evolution equations

Many nonlinear evolution equations can be converted into first- or high-order ordinary differential equations. In this paper, we illustrate a connection between the elliptic integrals and some nonlinear evolution equations such as the two-dimensional Boussinesq equation, and demonstrate that traveling wave solutions and periodic wave solutions to these nonlinear equations can be obtained by means of the standard forms of elliptic integrals directly.