Periodic solutions from Lie symmetries for the generalized Chen–Lee–Liu equation
Institute of Systems Science, Durban University of Technology, PO Box 1334, 4000, Durban, Republic of South Africa
2 Instituto de Ciencias Fisicas y Matematicas, Universidad Austral de Chile, 5090000, Valdivia, Chile
Accepted: 5 September 2021
Published online: 13 September 2021
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 behavior 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 supports the result for the existence of periodic behavior of the solutions.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021