Bright and dark optical chirp waves for Kundu-Eckhaus equation using Lie group analysis

In this study, the Kundu-Eckhaus represents the propagation of femtosecond light pulse in optical fibers is solved using symmetry technique. As a result, a finite Lie group of four vector fields is yielded. Then a similarity transformation is obtained using a linear combination of the four vector fields, which considers the general transformation for any used transformation before. According to that, the Kundu-Eckhaus is reduced to an auxiliary equation. By solving the auxiliary equation many novel solitary wave solutions were obtained. Finally, the propagation of the amplitude bright soliton is discussed, and it was found that the chirp wave depends on the amplitude function and is affected by the sign of the Raman parameter.