報(bào)告人：王雷 教授

報(bào)告題目：Super-regular breathers induced by the higher-order effects in coupled Hirota equations

報(bào)告時(shí)間：2026年1月17日（周六）下午15：00

報(bào)告地點(diǎn)：云龍校區(qū)智華樓205報(bào)告廳

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

王雷，畢業(yè)于北航流體力學(xué)研究所，英國(guó)愛(ài)丁堡大學(xué)數(shù)學(xué)系訪(fǎng)問(wèn)學(xué)者，華北電力大學(xué)教授、博士生導(dǎo)師。近年來(lái)主要研究方向?yàn)榉蔷€(xiàn)性波的計(jì)算與機(jī)制分析，人工智能在非線(xiàn)性動(dòng)力學(xué)中的應(yīng)用，人工智能在熱防護(hù)和能源環(huán)保數(shù)字孿生系統(tǒng)中的應(yīng)用等。主持國(guó)家自然科學(xué)基金四項(xiàng)，博士后基金面上和特助兩項(xiàng)，中央高?；鹑?xiàng)，相關(guān)結(jié)果發(fā)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(xué)術(shù)刊物。擔(dān)任國(guó)家自然科學(xué)基金評(píng)議人，教育部學(xué)位中心專(zhuān)業(yè)學(xué)位水平評(píng)估專(zhuān)家以及Nonlinearity, Proceedings of the Royal Society A, Journal of Optics, Ocean Engineering等多個(gè)學(xué)術(shù)期刊的評(píng)審人。

報(bào)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.