Envelope breather solution and envelope breather lattice solutions to the NLS equation

In this Letter, dependent and independent variable transformations are introduced to solve the nonlinear Schrödinger (NLS) equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the NLS equation, including many kinds of envelope breather solutions and envelope breather lattice solutions.