Optical solitary wave solutions in generalized determinant form for Kundu-Eckhaus equation

The Kundu-Eckhaus (KE) equation describes the propagation of ultra-short femtosecond pulses in optical fibers. In this paper, on the basis of Hirota bilinear form of KE equation, a complex matrix is introduced into the differential relation satisfied by determinant elements. By constructing relations among the matrix elements, the solution in generalized double Wronskian determinant form for the KE equation is derived. When the complex matrix introduced in the differential relation of the determinant elements take diagonal matrix and Jordan block matrix respectively, the soliton solutions and Jordan block solutions of the KE equation are obtained and propagation situations are discussed via different parameters.