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

Abstract

The generalized nonlinear Schrödinger equation (GNLS) iu t + u xx + β∣ u∣ 2 u + γ∣ u∣ 4 u + iα (∣ u∣ 2 u) x + iτ(∣ u∣ 2) x u = 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.