Periodic solitons of generalized coupled nonlinear Schrödinger equations with variable coefficients

Under investigation in this research is a generalized coupled nonlinear Schrödinger (vcGCNLS) equations with self-phase modulation, cross-phase modulation and four-wave mixing term in a birefringent fiber, which also include time-dependent diffraction, nonlinearity and gain (loss) parameters. By making full use of the developed Hirota bilinear method, we derive the bilinear forms and construct the periodic one-soliton and two-soliton solutions for this coupled equations. Based on the obtained periodic soliton solutions, the dynamical behaviors of them are analyzed. The results show that periodic solitons of different shapes can be designed by setting the diffraction effect σ ( t ) and the nonlinear effect R ( t ), which could result different gain (loss) parameter κ ( t ) , to different functions.