Multiphase and rational solutions of a family of nonlinear equations

A family of nonlinear partial differential equations with solutions having moving poles of first order is studied. It is shown that, depending on the relationships between the coefficients of the equations, this family has multiphase and rational solutions or is integrable. The structure of the exact solutions of the nonintegrable equations is described, and the connection is established between the order of the original nonintegrable equation and the existence of a multiphase solution.