Eur. Phys. J. D 58, 327-332 (2010)
https://doi.org/10.1140/epjd/e2010-00102-0

Self-similar cnoidal and solitary wave solutions of the (1+1)-dimensional generalized nonlinear Schrödinger equation

¹ School of Sciences, Zhejiang Forestry University, Linan, Zhejiang, 311300, P.R. China
² School of Physical Science and Technology, Suzhou University, Suzhou, Jiangsu, 215006, P.R. China

Corresponding authors: ^a lhzhao@zjfc.edu.cn - ^b dcq424@126.com

Received: 25 October 2009
Revised: 24 December 2009
Published online: 26 April 2010

Abstract

With the help of the similarity transformation and the solvable stationary nonlinear Schrödinger equation (NLSE), we obtain exact chirped and chirp-free self-similar cnoidal wave and solitary wave solutions of the generalized NLSE exhibiting spatial inhomogeneity, inhomogeneous nonlinearity and gain or loss at the same time. As an example, we investigate their propagation dynamics in a nonlinear optical system, and present a series of interesting properties of optical waves.