Nonlinear Dynamic of Localized Structures

我们研究了1，非线性介质中的局域结构，2，非线性动力系统的模拟，3，局域结构的动力学。主要结果如下：(1)用几何模型作为晶体生长的模型，发现了一些新的精确解。(2)离子声孤子无时滞地穿过鞘区。(3)通过改变起搏器的半径可以控制目标方向图的波长。(4)动力学系统中团簇结构的形成与系统的混沌特性密切相关，并通过混沌的存在来维持这种结构。(5)基于磁声屋檐加速机制，解释了太阳高能粒子的基本性质。(6)模拟地球和太阳中磁场的产生机制，发现偶极子场是由对流运动产生的。(7)利用双线性形式，可以对孤子方程进行系统的离散，保持可积性。(8)推导了离子波的二维非线性薛定谔方程，并找到了描述重联的新解。

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.