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The nonlinear generalized Chen-Lee-Liu 1+1 evolution equation which describesthe propagation of an optical pulse inside a monomode fiber is studied by usingthe method of Lie symmetries and the singularity analysis. Specifically, wedetermine the Lie point symmetries of the Chen-Lee-Liu equation and we reducethe equation by using the Lie invariants in order to determine similaritysolutions. The solutions that we found have periodic behaviour and describeoptical solitons. Furthermore, the singularity analysis is applied in order towrite algebraic solutions of the Chen-Lee-Liu with the use of Laurentexpansions. The latter analysis support the result for the existence ofperiodic behaviour of the solutions.

Periodic solutions from Lie symmetries for the generalized Chen-Lee-Liu equation