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）
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）
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.
主讲人：林机 教授，硕士生导师 （浙江师范大学）
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）
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.
主讲人：任博 博士 （绍兴文理学院）
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
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
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）
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.
主讲人：刘希忠 博士 （绍兴文理学院）