Nonlinear Dynamic of Localized Structures

我们研究了1、非线性介质中的局部结构；非线性动力系统仿真，3。局部结构动力学。主要研究结果总结如下：(1)用几何模型作为晶体生长可积系统的模型，得到了一些新的精确解。(2)离子声孤子无时间延迟地穿过鞘区。(3)通过改变起搏器的半径，可以控制目标图案的波长。(4)动力系统簇状结构的形成与系统的混沌特性密切相关，混沌的存在维持了簇状结构。(5)基于磁声波加速机制，解释了太阳高能粒子的基本性质。(6)模拟地球和太阳磁场的形成机制，发现偶极子场是由对流运动形成的。(7)利用双线性形式，可以系统地保持孤子方程的可积性。(8)导出了离子波的二维非线性薛定谔方程，并给出了描述离子波重连的新解。

We have investigated 1, localized structures in nonlinear media, 2.simulations of nonlinear dynamical systems, 3.dynamics of localized structures. The main results are summarized as follows.(1)Using a Geometrical model as a model for crystal growths intergrable systems and found some new exact colutions.(2)Ion acoustic solitons oass through the sheath region without a time delay.(3)A wave length of target pattern can be controlled by changing a radius of pacemaker.(4)Formation of cluster structure in dynamical system is clisely related to the chaotic property of the system and the structure is maintained by the existence of chaos.(5)Based on a mechanism of magnetosonic sound eave scceleration, the fundamental properties of solar tigh energy particles are explained.(6)Simulating the creation mechanism of magnetic fields in the earth and the sun, we found that the dipole field is developed by the convection motions.(7)By use of a bilinear formalism, the discretization of soliton equation can bbe done systematicakky preserving intergrability.(8)Two dimensional Nonlinear Schrodinger equation is derived for ion waves and its new solution describing the reconnection is found.