Sine-Gordon方程的截断系统的同宿轨道  

HOMOCLINIC ORBITS OF THE TRUNCATED SYSTEMS OF SINE-GORDON EQUATION 1)

作　　者：徐振源[1,2,3] 刘曾荣[1,2,3] 

机构地区：[1]无锡轻工业大学数学物理研究所 [2]中国科学院力学研究所LNM开放实验室 [3]苏州大学数学科学学院

出　　处：《力学学报》1998年第3期292-299,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金

摘　　要：研究ＳｉｎｅＧｏｒｄｏｎ方程的广义渐近惯性流形上的常微分方程组，证实了在一定参数条件下存在Ｗｉｇｇｉｎｓ［１］意义下的同宿轨道．计算表明，与Ｂｉｓｈｏｐ［２］用数值计算得到的ＳｉｎｅＧｏｒｄｏｎ方程产生混沌的参数值尚有差别，考虑到同宿出现参数值往往低于混沌出现参数值，故结果在定性上正确，而且改进了文［１］中的结果．In this paper the existence of the homoclinic orbits defined by Wiggins is proved, by use of ODE on the generalized asymptotic inertial manifold for the Sine Gordon equation. We give explicit conditions (in terms of the system parameters) for the model to possess a symmetric pair of homoclinic orbits to a fixed of saddle focus type, chaotic dynamics follow from a theorem of Silnikov. This provides a mechnism for chaotic dynamics geometrically similar to that observed by Bishop et al.,namely, a random “jumping” between two spatially dependent states with an intermediate passage through a spatially independent state. It is showed that our parameters values are little different to Bishop'svalues, since the parameter values for homoclinic values always smaller than the parameter values for chaos, our results are right onqualitative analysis and correct the results of (1).

关 键 词：无穷维 动力系统 S-G方程 同宿轨道 非线性 

分 类 号：O302[理学—力学] O175.2