非线性物理系列学术讲座通知

发布时间：2018-01-16 作者： 来源：电子信息学院

时间：2018-01-20上午8:30-12:00，下午3:00-6:00

地点：厚德楼A809会议室

举办单位：电子信息学院

讲座一：Alice-Bob Physics: Coherent Solutions of Nonlocal KdV Systems

主讲人：楼森岳 教授，博士生导师 （宁波大学、华东师范大学）

讲座内容简介：

In natural and social science, many events happened at different space-times may be closely correlated. Two events, A (Alice) and B (Bob) are defined correlated if one event is determined by another. Taking KdV and coupled KdV systems as examples, we can find some types of models (AB-KdV systems) to exhibit the existence on the correlated solutions linked with two events. The idea of this report is valid not only for physical problems related to KdV systems but also for problems described by arbitrary continuous or discrete models. The parity and time reversal symmetries are extended to shifted parity and delayed time reversal. The new symmetries are found to be useful not only to establish AB-systems but also to find group invariant solutions of numerous AB-systems. A concrete AB-KdV system derived from the nonlinear inviscid dissipative and barotropic vorticity equation is applied to the two correlated monople blocking events which is responsible for the snow disaster in the winter of 2007/2008 happened in Southern China.

讲座二： Nonlocal symmetry and similarity reductions for the Drinfeld Sokolov Satsuma Hirota system

主讲人：陈勇 教授，博士生导师 （华东师范大学）

讲座内容简介：

The nonlocal symmetry of the Drinfeld–Sokolov–Satsuma–Hirota system is obtained from the known Lax pair, and infinitely many nonlocal symmetries are given by introducing the internal parameters. Then the nonlocal symmetry is localized to a prolonged system by introducing suitable auxiliary dependent variables. By applying the classical Lie symmetry method to this prolonged system, two main results are obtained: a new type of finite symmetry transformation is derived, which can generate new solutions from old ones; some exact interaction solutions among solitons and other complicated waves including periodic cnoidal wave and Painleve waves are derived through similarity reductions.

讲座三：孤立子理论在非线性光学中的解析解研究

主讲人：林机 教授，硕士生导师 （浙江师范大学）

讲座内容简介：

研究空间光孤子在一维竞争非局域三次五次非线性介质中的新解和传输特性．发现亮孤子在竞争非局域三次自散焦和五次自聚焦非线性介质中存在不稳定区间．在一般非局域程度下，对于不同的三次非线性效应，同相位复合两孤子间表现为吸引或排斥的相互作用，并讨论了折射率的变化．在竞争非局域三次自聚焦和五次自散焦非线性介质中给出了二极、三极和四极孤子能稳定传播的条件，研究发现更高极孤子的传播是不稳定的．还研究了孤子功率与传播常数以及非局域程度的关系．

讲座四：New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

主讲人：姚若侠 教授，博士生导师 （陕西师范大学）

讲座内容简介：

Motivated by the widely used ansatz method and starting from the modified Riemann Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.

讲座五：The Painleve analysis and exact solutions for the supersymmetric Ito equation

主讲人：俞军 教授，硕士生导师 （绍兴文理学院）

讲座内容简介： A singularity structure analysis for the supersymmetric Ito (sIto) system is carried out. It demonstrates that the sIto system admits the Painleve property. Meanwhile, the sIto system is changed to a system of coupled bosonic equations based on the bosonization approach. The exact solutions of the sIto system are obtained with the mapping and deformation method and the similarity reduction method.

讲座六：超mKdV方程：玻色化、Painleve性质和精确解

主讲人：任博 博士 （绍兴文理学院）

讲座内容简介：

The symmetry of the fermionic field is obtained by means of the Lax pair of the mKdV equation. A new super mKdV equation is constructed by virtue of the symmetry of the fermionic form. The super mKdV system is changed to a system of coupled bosonic equations with the bosonization approach. The bosonized SmKdV (BSmKdV) equation admits Painlev′e property by the standard singularity analysis. The traveling wave solutions of the BSmKdV system are presented by the mapping and deformation method. We also provide other ideas to construct new super integrable systems.

讲座七：General high-order breathers, lumps in the (2+1)-dimensional Boussinesq equation

主讲人：李彪 教授，硕士生导师（宁波大学）

讲座内容简介：

By employing the Bell's polynomials, bilinear formalism of the (2+1)-dimensional Boussinesq equation is succinctly constructed. Furthermore, based on the bilinear formalism, general high-order breather solutions are obtained by using the Hirota's bilinear method with the perturbation expansion. These breathers are periodic in x direction and localized in y direction. Taking a long wave limit of the obtained breather solutions and then making further parameter constraints, smooth rational solutions are generated. These smooth rational solutions are high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. These results exhibit the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.

讲座八：Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system

主讲人：唐晓艳 博士，硕士生导师（华东师范大学）

讲座内容简介： A new general nonlocal modified KdV equation is derived from the nonlinear inviscid dissipative and equivalent baratropic vorticity equation. The nonlocal property is manifested in the shifted parity and delayed time reversal symmetries. Exact solutions of the nonlocal modified KdV equation are obtained including periodic waves, kink waves, solitary waves, kink- and/or anti-kink-cnoidal periodic wave interaction solutions, which can be utilized to describe various two-place and time-delayed correlated events. As an illustration, a special approximate solution is applied to theoretically capture the salient features of two correlated dipole blocking events in atmospheric dynamical systems.

讲座九：Dust Acoustic Waves in Magnetized Dense Plasmas with Dust-neutral Collisions

主讲人：杨建荣 教授，硕士生导师 （上饶师范学院）

讲座内容简介：

In order to study the characteristics of dust acoustic waves in a uniform dense dusty magnetoplasma system, a nonlinear dynamical equation is deduced using the quantum hydrodynamic model to account for dust–neutral collisions. The linear dispersion relation indicates that the scale lengths of the system are revised by the quantum parameter, and that the wave motion decays gradually leading the system to a stable state eventually. The variations of the dispersion frequency with the dust concentration, collision frequency, and magnetic field strength are discussed. For the coherent nonlinear dust acoustic waves, new analytic solutions are obtained, and it is found that big shock waves and wide explosive waves may be easily produced in the background of high dusty density, strong magnetic field, and weak collision. The relevance of the obtained results is referred to dense dusty astrophysical circumstances.

讲座十：若干非线性系统的留数对称约化

主讲人：刘希忠 博士 （绍兴文理学院）

讲座内容简介：

利用扩展系统的方法将留数对称局域化然后利用经典对称理论可以得到非线性系统的新的对称约化解，其中包括相互作用解。

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