LAUSR

Abstract We consider the perturbed Chen-Lee-Liu equation for describing propagation pulse in optical fiber. The Cauchy problem for this equation is not solved by the inverse scattering transform and we study this equation using the traveling wave reduction. We show that there are two first integrals for the system of equations corresponding to real and imaginary parts of the perturbed Chen-Lee-Liu equation. These first integrals are used to obtain the nonlinear first-order differential equation. The general solution of the first-order ordinary differential equation is found via the Weierstrass and Jacobi elliptic functions. Periodic and solitary waves of the perturbed Chen-Lee-Liu equation in the form of the traveling reduction are presented and illustrated.