Cubic–quartic nonlinear Schrödinger equation in birefringent fibers with the presence of perturbation terms

Abstract

ABSTRACT In this paper, we derive the solitons solutions to the cubic–quartic nonlinear Schrödinger equation (CQ-NLSE) in birefringent fibers with three laws of nonlinearity. These laws are parabolic law, quadratic-cubic law and non-local law. The new extended generalized Kudryashov method and our new method proposed for the first time have been applied. Many solutions have been found. Dark, bright and singular soliton solutions existed under constraint conditions. The comparative analysis of the two proposed methods shows that in the two cases of parabolic and non-local laws, the first method gives the dark and singular solitons in terms of tanh–coth hyperbolic functions, respectively, while the second method gives the bright and singular solitons in terms of sech–csch hyperbolic functions, respectively. But in the case of quadratic-cubic law, both methods give the bright-singular solitons in terms of sech–csch hyperbolic functions, respectively, with different arguments.