报告人：王雷 教授
报告题目：Super-regular breathers induced by the higher-order effects in coupled Hirota equations
报告时间：2026年1月17日（周六）下午15：00
报告地点：云龙校区智华楼205报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
王雷，毕业于北航流体力学研究所，英国爱丁堡大学数学系访问学者，华北电力大学教授、博士生导师。近年来主要研究方向为非线性波的计算与机制分析，人工智能在非线性动力学中的应用，人工智能在热防护和能源环保数字孪生系统中的应用等。主持国家自然科学基金四项，博士后基金面上和特助两项，中央高校基金三项，相关结果发表在Physica D, Proceedings of the Royal Society A, Physical Review E, Chaos, Annals of Physics, Physics of Plasmas, EPL, PLA等重要学术刊物。担任国家自然科学基金评议人，教育部学位中心专业学位水平评估专家以及Nonlinearity, Proceedings of the Royal Society A, Journal of Optics, Ocean Engineering等多个学术期刊的评审人。
报告摘要：
We study the intriguing dynamics of surper-regular breathers (SRBs) beyond the Manakov system. These SRB solutions are derived within the nondegenerate context. By employing the Darboux transformation, we obtain the exact expressions of the solutions for the vector SRBs in the coupled Hirota equations with the third dispersion, self-steepening, and inelastic Raman scattering terms. Based on such explicit formulas, we initially study the higher-order effects on their group velocities as well as the growth rate during the linear stage of modulation instability (MI). Additionally, we conduct an exploration of various mode excitations emerging during the nonlinear stage of MI. Our findings indicate that there exist significantly different wave modes from those in the Manakov system or the scalar nonlinear Schrödinger equation (NLSE). In particular, we refine existing formulas connecting the SRBs and MI in the nondegenerate regime, which eliminates the necessity to neglect higher-order terms from the Taylor expansion of α. Instead, we have used four different eigenvalues for a more comprehensive description. We also discuss the scalar SRB with two eigenvalues using wave component analysis. We finally excite, via numerical simulation initiated with localized periodic initial conditions, the vector SRBs and their transformed states. This study not only deepens our theoretical comprehension of SRB dynamics, but also illuminates potential avenues for future experimental investigations in this fascinating field.
