Sn-cn, sn-dn, cn-dn Jacobi elliptic functions and solitons solutions in birefringent fibers for CGL equations with Hamiltonian perturbations and Kerr law nonlinearity

Abstract

The current work is dedicated to the investigation of the propagation of progressive solitons in birefringent fibers for Complex Ginzburg–Landau equations with Hamiltonian perturbations and Kerr law nonlinearity. To achieve this goal, we use a modified F-expansion method which enables us to widen the class of solutions to these coupled equations and permit the propagation of different waves on the two lines. First of all, we constructed the solutions in terms of Jacobi elliptic functions in the forms of dn-sn, dn-cn, and cn-sn. After that, we obtained the progressive soliton solutions in the limiting approach, when the modulus of ellipticity approaches unity. These progressive soliton solutions include bright–dark, bright–bright, dark–dark, bright–front, dark–front. For these solutions to exist, the criteria are exhibited in form of parameter constraints. In addition, the visual representations of these solutions depicted in several figures surely play a key part in understanding the behavior and capturing some of the physical aspects of the model under consideration.