Nonlinear Dynamic of Localized Structures

局部结构的非线性动力学

• 批准号: 03302018
• 负责人: WADATI Miki
• 金额: $ 9.73万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03302018/
• 关键词: Soliton; Chaus; Vortex; Hirota Method; Pattern Formation; Nonlinear Waves; Soliton Eguations; Motion of Curves and Surfaces; 曲線、曲面の運動; 非線形シュレディンガー方程式; 広田の直接法; 構造形成; イオン高波; 反応拡散系; 渦系; 非線形力学系; 磁気リコネクション; 結び目理論; 非線形シュレディンガ-方程式

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.

我们研究了1.非线性介质中的局域结构，2.非线性动力学系统的模拟，3.局域结构的动力学。主要研究结果如下。（1）用几何模型作为晶体生长的数学模型，建立了可积系统的数学模型，并得到了一些新的精确解。（2）离子声孤子在鞘层中的传播没有时间延迟。(3)A目标图案的波长可以通过改变起搏器的半径来控制。（4）动力学系统中团簇结构的形成与系统的混沌性密切相关，而团簇结构的形成是由混沌的存在来维持的。（5）从磁声屋檐加速的机理出发，解释了太阳高能粒子的基本性质。（6）模拟了地球和太阳磁场的产生机制，发现偶极子磁场是由对流运动产生的。(7)By利用双线性形式，孤子方程的离散化可以系统地保持可积性。（8）导出了离子波的二维非线性薛定谔方程，并求出了描述重联的新解。

项目成果

Y.Yoshida: "Observation of the Plasma Lens Effect" Particle Accel.39. 77-87 (1992)

Y.Yoshida：“等离子透镜效应的观察”粒子加速.39。

M.FUNAKOSHI: "Bifurcations in Resonantly Forced Water Waves" Eur.J.Mech.B/Fluids. 10. 31-36 (1991)

M.FUNAKOSHI：“受迫共振水波中的分叉”Eur.J.Mech.B/Fluids。

M.Oikawa: "Effect of the Thind-Order Dispersion on the Nonlinear-Schrodinger Equation" J.Phys.Soc.Jpn.62. 2324-2333 (1993)

M.Oikawa：“薄阶色散对非线性薛定谔方程的影响”J.Phys.Soc.Jpn.62。

T.X.Zhang: "Oblique Ion Acoustic Wave Instabilities and ^3He-Rich Events" J.Phys.Soc.Jpn.62. 2545-2548 (1993)

T.X.Zhang：“斜离子声波不稳定性和^3He-Rich事件”J.Phys.Soc.Jpn.62。

R.Hirota et al.: "Future Directions of Nonlinear Dynamics in Physical and Biological Systems" (Plenum Press), (1993)

R.Hirota 等人：“物理和生物系统中非线性动力学的未来方向”（Plenum Press），（1993）