低模态下弱阻尼KdV方程约化形式的数值分析

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

基金项目: 国家自然科学基金资助项目(19601020;19872044);江苏省青年科技基金资助项目(BK97119;BQ98023);江苏省青蓝工程基金

Numerical Analysis of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation

1.
Department of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212013, P. R. China;
2.
Department of Mathematics, Wuxi University of Light and Industry, Wuxi, Jiangsu 214036, P. R. China;
3.
Department of Mathematics, Shanghai University, Jiading, Shanghai 201800, P. R. China;
4.
Department of Mathematics, Nanjing University of Science and Technology, Nanjing 210000, P. R. China

摘要: 给出了低模态下弱阻尼KdV方程近似惯性流形的约化形式,并在五模态下作数值分析,有关数值分析结果与非线性谱分析结果相类似
- 周期边界条件 /
- 偏微分方程 /
- 动力系统 /
- 孤立波/近似惯性流形
Abstract: The numerical analysis of the appro ximate inertial manifold in weakly damped fo rced KdV equation is given. The results of numerical analysis under five models is the same as that of nonline ar spectral analysis.
- periodic boundary conditions /
- partial differential equation /
- dynamical systems /
- soliton/approx imate inertial manifold

[1]	Temam R.Infinite Dimensional Systems in Mechanics and Physics[M].Berlin:Springer-Verlag,1988.
[2]	Constantin P,Foias C,Nicolaenko B,et al.Integral Manifolds and Inerital Manifolds for Dissipative Partial Differential Equations[M].Berlin:Springer-Verlag,1988.
[3]	Cross M C,Hohenberg P C.Pattern formation of equilibrium[J].Rev Modern Phys,1993,65(2):851-1223.
[4]	田立新,徐振源.弱阻尼KdV方程长期动力学行为研究[J].应用数学和力学,1997,18(10):953-958.
[5]	Ercolani N M,Mclaughin D W,Roitner H.Attractors and transients for a perturbed periodic KdV equations:a nonlinear spectral analysis[J].J Nonlinear Science,1993,3(2):477-579.