Asymptotic analysis of double-hump solitons for a coupled fourth-order nonlinear Schrödingier system in a birefringent optical fiber

Double-hump solitons can be used as a coding method for information transmission, thereby enhancing the data transmission capacity. In this paper, we investigate a coupled fourth-order nonlinear Schrödinger system which describes the propagation of ultrashort optical pulses in a birefringent optical fiber. Based on the solutions we obtained, we acquire the relative velocity of two solitons related to the strength of higher-order linear and nonlinear effects ξ. When the relative velocity approaches 0, we present the double-hump nondegenerate soliton. Via the asymptotic analysis, we obtain the amplitudes, phase shifts and velocities of two solitons, and find that the overall intensity of each soliton is maintained invariant before and after the interaction. According to whether the amplitude changes or not, we accordingly illustrate the inelastic and elastic interactions between two solitons. Via the three-nondegenerate soliton solutions, we obtain the inelastic interaction with the internal oscillations of the double-hump and single-hump solitons. We find that the velocity of single-hump soliton is dependent on ξ, amplitude and phase shift are independent of ξ. Via the four-nondegenerate soliton solutions, we get the inelastic interaction without the internal oscillations of the double-hump and single-hump solitons, and elastic interaction of two double-hump solitons. The insights gained from this study of the double-hump nondegenerate soliton interactions maybe not only enrich the fundamental theory of nonlinear waves but also provide a foundation for using the properties of double-hump nondegenerate solitons in the potential technological applications within optics.