Breather Solutions Of The Discrete Nonlinear Schr(o|¨)dinger Equations In Inhomogeneous Media

This paper is concerned with breather solutions of the discrete nonlinear Schro¨dingerequations in inhomogeneous media. In first part, the one-dimensional Schro¨dinger equationis considered. By using a constrained minimization approach known as the Nehari variationalprinciple or the Nehari manifold approach, we obtain the existence of nontrivial breathersolutions and the property of exponential decay. In second part, the special m-dimensionalShcro¨dinger equation is considered. The same method as the first part is used to investigatethe breather solutions.