報告人：王雷 教授

報告題目：Super-regular breathers induced by the higher-order effects in coupled Hirota equations

報告時間：2026年1月17日（周六）下午15：00

報告地點：云龍校區智華樓205報告廳

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

王雷，畢業于北航流體力學研究所，英國愛丁堡大學數學系訪問學者，華北電力大學教授、博士生導師。近年來主要研究方向為非線性波的計算與機制分析，人工智能在非線性動力學中的應用，人工智能在熱防護和能源環保數字孿生系統中的應用等。主持國家自然科學基金四項，博士后基金面上和特助兩項，中央高校基金三項，相關結果發表在Physica D, Proceedings of the Royal Society A, Physical Review E, Chaos, Annals of Physics, Physics of Plasmas, EPL, PLA等重要學術刊物。擔任國家自然科學基金評議人，教育部學位中心專業學位水平評估專家以及Nonlinearity, Proceedings of the Royal Society A, Journal of Optics, Ocean Engineering等多個學術期刊的評審人。

報告摘要：

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 Schr?dinger 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.