Degenerate soliton solutions and their dynamics in a coupled generalized nonlinear Schrödinger equations with the four-wave mixing effect

Abstract

Energy distribution of the degenerate solitons is more concentrated, they are more resistant to external disturbances (such as the noise and dispersion). This paper investigates the degenerate soliton solutions for coupled generalized nonlinear Schrödinger equations with the four-wave mixing effect in a birefringent fiber. Since the interactions of degenerate solitons in this equations are not studied, this paper investigate the properties and inelastic interactions of degenerate solitons. We construct the two-, three- and four-degenerate soliton solutions with one and two spectral parameters. According to the asymptotic analysis method, we find that the amplitudes of the interacting solitons retain unchanged upon the interactions, thus the elastic interactions between two degenerate solitons are depicted. Relative distance between two asymptotic solitons exhibits logarithmic growth with $\left|t\right|$, where $t$ represents the retarded time. Soliton separation acceleration decays exponentially with relative distance, eventually tends to zero. Phase shifts vary slowly with $t$. Elastic and inelastic interactions of three and four degenerate solitons with multiple iterations of one and two spectral parameters are presented. Different from the previous literary works, this paper solves the degenerate soliton solutions of this equations using the multiple spectral parameters and obtains some inelastic interactions. Elastic interactions may provide a technical foundation for the high fidelity information transmission. Inelastic interactions may have wide applications in the energy conversion and signal processing. This paper may be helpful for understanding the soliton propagation characteristics in the nonlinear media.