Analytical Study of Nonlinear Evolution Equation

In present work, we study the well-known Vakhnenko equation using a new function expansion method which can be thought of as the generalization of (G^’/G)expansion given by M. Wang et al recently. We call it (Θ/g) expansion method. The Vakhnenko equation describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko Equation are obtained.