近日，燕山大学的徐天赋课题组取得一项新进展。经过不懈努力，他们研究了一维非线性周期系统中二次与四次色散竞争下的带隙孤子。相关成果已于2023年7月18日在国际知名学术期刊《物理评论A》上发表。

该团队研究了在二次与四次色散竞争条件下的Kerr非线性系统中的带隙孤子和非线性布洛赫波。研究结果表明，非线性布洛赫波可以视为无限基态带隙孤子链。研究人员通过数值分析揭示了相关带隙中带隙孤子的性质，并发现色散系数的变化导致了带隙孤子功率关系的变化，特别是对于第一个带隙中的两个经典偶极子模式。

通过分析基态带隙孤子之间的相互作用，研究人员获得了带隙波的稳定区间变化规律，与线性稳定性分析和实时数值监测结果一致。这一研究为进一步探究高阶色散下高阶孤子的物理性质提供了启示。

附：英文原文

Title: Gap solitons with quadratic and quartic dispersion competition in one-dimensional nonlinear periodic systems

Author: Y. Cao, T. F. Xu

Issue&Volume: 2023/07/18

Abstract: We studied gap solitons and nonlinear Bloch waves in Kerr nonlinear systems under competition between quadratic and quartic dispersions. The results show that nonlinear Bloch waves can still be regarded as infinite fundamental gap solitons chains. We also revealed the properties of the gap solitons in the relevant band gaps by numerical analysis. Notably, for the two classical dipole modes in the first gap, the variation of the dispersion coefficient leads to the change of the soliton power relation due to the interaction between the two solitons composing them. We obtained the stable interval variation rule of gap waves without calculation by analyzing the interaction between fundamental gap solitons. This is consistent with our linear stability analysis and real-time numerical monitoring results. This finding provides an idea for further investigation of the physical properties of higher-order solitons under higher-order dispersion.

DOI: 10.1103/PhysRevA.108.013509

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.108.013509