耗散KdV方程的小波近似惯性流形及数值分析

利用田立新提出的小波近似惯性流形 ,将小波分析与无穷维动力系统相结合研究一类非线性孤立波方程 -耗散KdV方程的长期动力学行为 ,在已得到该类方程存在小波近似惯性流形及利用无穷维动力系统作更精确的误差估计的基础上 ,笔者用L2 (R)中Perrier -Bas devant样条周期小波基做小波分析 ,用低模态的小波近似惯性流形数值模拟耗散KdV方程的吸引子 数值结果表明 ,小波近似惯性流形方法比Fourier分析方法及小波Galerkin方法更能反映系统的局部动力学行为

Wavlet Approximate Inertial Manifold and Numerical Analysis of Dissipative KdV Equation

In this paper, using the wavelet approximate inertial manifo ld introduc ed by Tian Lixin, the author studies the long time dynamics behavior for a sort of nonlinear solitary wave equation-dissipative KdV equation by connecting the wavelet analysis and infinite dimensional dynamics system. On the basis of more accurate error estimate attained with infinite dimensional dynamics system, the paper makes wavelet analysis for Perrier-Basdevant spline periodic wavelet basi s and describes the attractor of dissipative KdV equation for using low model wav elet approximate inertial manifold to give numerical simulation. T he method of wavelet approximate inertial manifold is proved superior to the Fou rier analysis and wavelet Galerkin Method in the local dynamics behavior .