周天寿
论文题目：激励介质中非线性波型动力学的研究
作者简介：周天寿，男，1962年05月出生，1998年09月师从于中国科学院数学与系统科学研究院张锁春教授，于2001年08月获博士学位。
摘 要
该论文以刻划Belousov-Zhabotinsky化学反应的Oregonator模型为主线, 致力于激励介质中非线性波型动力学的理论研究.主要结果包括:
(1)解决了Tyson于1979年提出关于耦合Oregonator振子分歧图的一个猜想.其证明过程实际上给出了处理类似问题的一般方法.
(2)在波前邻域内，建立一新的运动坐标系, 获得了在直角坐标系下的Eikonal方程，不仅容易求出一些常见的波型解，而且可以刻划波的曲率效应.
(3)借助Painlevě分析和Bäcklund变换, 首次给出了行波或平面波的波速和色散关系在薄的边界层内的显式表示。应用奇异摄动方法,给出了包括螺旋波和靶型波在内的一些非线性波型解的形式。
(4)首次给出了组织中心沿径向和轴向运动所遵守的线性律中系数的显式表示,由此容易判断组织中心沿径向运动是否为扩张或收缩, 沿轴向运动是否为正向漂移或反向漂移.
(5)证明了激励介质中某些波的存在性和稳定性，并深刻研究了Oregon-ator模型所对应的常微分方程的动力行为,获得了 很好的结果。
RESEARCH
ON DYNAMICS OF NONLINEAR WAVE PATTERN IN EXCITABLE MEDIA (EM)
Abstract
This thesis works for theoretical study on dynamics of nonlinear wave pattern in EM by taking the Oregonator model portraying Belousov-Zhabotinsky chemical reaction as an example. The main results contain:
(1) Solving Tyson's conjecture on bifurcation diagram in linearly coupled Oregonator. The proof procedure on it practically gives a general method to deal with the analogous problems.
(2) Through establishing a new moving coordinate system in the neighborhood of the wave front, obtaining a revised eikonal equation in the usual orthogonal coordinate system, from which one can find not only some usual wave pattern solutions and but also describe the curvature effect of waves.
(3) With Painleve analysis and Bäcklund transformation technic,first obtain-obtaining explicit expressions of wave speed and dispersion relation within thin boundary layer, and by using perturbation method, first giving forms of some nonlinear wave solutions including spiral waves and targets
(4) First giving explicit representations of coefficients in linear rules obeyed by motion of the organizing filament. It demonstrates whether the filament expands or shrinks along the radial direction, and whether positively or inversely shifts along the axial direction.
(5) Proving existence and stability of some waves in EM. Besides, proceeding deep study on dynamical behavior in the relative ordinary differential equations and obtaining some nice results.
