Exact solitary and periodic wave solutions for a generalized nonlinear Schrödinger equation

The generalized nonlinear Schrödinger equation (GNLS) iut + uxx + β∣u∣2u + γ∣u∣4u + iα (∣u∣2u)x + iτ(∣u∣2)xu = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation. Int J Bifucat Chaos 2005:3295–305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.