Optical solitons to Kundu–Eckhaus equation in birefringent fibers without four-wave mixing

This paper investigates the soliton solutions of Kundu–Eckhaus equation for birefringent fibers, by employing two resourceful integration techniques, which are extended (G′/G)-expansion method and extended direct algebraic method. Variety of exact traveling wave solutions are obtained through these integration schemes. These solutions include singular solitons, dark-singular solitons, rational solutions, combination of hyperbolic functions and trigonometric functions. Whereas, periodic singular solutions are obtained as by product of these methods. Some constraint relations pop out naturally that guaranty the existence of these solutions.