It is well known that nonlinear evolution equations (NLEEs) are widely used to describe physical phenomena in various scientific and engineering fields, such as fluid mechanics, plasma physics, optical fibers, biology, solid state physics, etc. In order to understand the mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. Solutions for the NLEEs can not only describe the designated problems, but also give more insights on the physical aspects of the problems in the related fields. In recent years, various powerful methods have been presented for finding exact solutions of the NLEEs in mathematical physics. The main purpose of this book is to illustrate how to establish solitary and periodic solutions of many NLEEs. Many illustrative examples are discussed by different methods, enjoy reading it.