## 学术预告：李继彬教授谈“Exact Solutions and Dynamics of the Raman Soliton Model in Nanoscale Optical Waveguides, with Metamaterials, Having Polynomial Law Non-Linearity”

Raman soliton model in nanoscale optical waveguides, with metamaterials, having polynomial law non-linearity are investigated by the method of dynamical systems. Because the functions $\phi(\xi)$ in the solutions $q(x,t)=\phi(\xi)\exp(i(-kx+\omega t)),\ (\xi=x-vt)$ satisfy a singular planar dynamical system having two singular straight lines. By using the bifurcation theory of dynamical systems, under different parameter conditions, bifurcations of phase portraits and exact periodic solutions, homoclinic and heteroclinic solutions, compacton solutions for this planar dynamical system can be given. Under given parameter conditions, solutions $q(x,t)$ can be exactly obtained. 92 exact explicit solutions of equation are derived.

李继彬，华侨大学特聘教授，博士生导师，动力系统与非线性研究中心负责人。1991年开始享受国务院政府特殊津贴。1998年国家人事部授予“国家有突出贡献专家”。曾任四届国家自然科学基金委数学学科评审专家组成员，云南省科学技术委员会常务委员，三届云南省数学会理事长，云南省应用数学研究所副所长，昆明理工大学理学院院长，昆明理工大学二级教授，浙江师范大学特聘教授等。