  The nonlinear generalized Chen-Lee-Liu 1+1 evolution equation which describes
the propagation of an optical pulse inside a monomode fiber is studied by using
the method of Lie symmetries and the singularity analysis. Specifically, we
determine the Lie point symmetries of the Chen-Lee-Liu equation and we reduce
the equation by using the Lie invariants in order to determine similarity
solutions. The solutions that we found have periodic behaviour and describe
optical solitons. Furthermore, the singularity analysis is applied in order to
write algebraic solutions of the Chen-Lee-Liu with the use of Laurent
expansions. The latter analysis support the result for the existence of
periodic behaviour of the solutions.
