Analytical bright soliton solutions of the nonlinear Schrödinger equation including both high-order diffraction effect and parabolic-law nonlinearity

By using the new Kudryashov method (NKM), we derived two bright soliton solutions of the nonlinear Schrödinger equation, which simultaneously includes high-order diffraction effects, parabolic-law nonlinearity and weakly nonlocal nonlinearity. The characteristics of the two soliton solutions were also studied in detail. The research results show that the diffraction effects, nonlinear coefficient and soliton wave number all have significant influences on the transmission dynamics characteristics of solitons. We can achieve long-distance transmission where the soliton maintains its shape and the center position unchanged by reasonably adjusting these parameters. The research reveals the synergistic mechanism among parameters and points out that maintaining the critical balance between the system parameters is a key challenge in practical applications. The relevant results in this paper provide certain theoretical support for the soliton transmission in complex nonlinear systems and offer a new perspective for the optimization of signal transmission in optical fiber communication.