Citation: | TIAN Li-xin, LIU Yu-rong, LIU Zeng-rong. The Research of Blow-up in 2D Weakly Damped Forced KdV Equation on Thin Domain[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1002-1008. |
[1] |
谷超豪.孤立子理论及应用[M].应用数学丛书,杭州:浙江大学出版社,1990.
|
[2] |
刘式适,刘式达,谭本馗.非线性大气动力学[M].北京:国防工业大学出版社,1996.
|
[3] |
郭柏灵.非线性演化方程[M].非线性科学丛书,上海:上海科技教育出版社,1995.
|
[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] |
Balmforth N L,Ierley G R,Worthing R.Pulse dynamics in unstable medium[J].SIAM J Appl Math,1997,57(1):205-251.
|
[6] |
Ghidaglia J M.Weakly damped forced Korteweg-de Vries equa tions be have as a finite dimensional dynamical system in the long time[J].J Differential Equations,1988,74(2):369-390.
|
[7] |
Ghidaglia J M.A note on the strong convergence towards at tractors of damped forced KdV equations[J].J Differential Equations,1994,110(2):356-359.
|
[8] |
卢殿臣,田立新,刘曾荣.扰动周期KdV方程的小波基分析[J].应用数学和力学,1998,19(11):975-979.
|
[9] |
Temam R,Wang S.Inertial form of Navier-Stokes equations on the sphere[J].J Funct Anal,1993,117(2):215-243
|
[10] |
LIU Zeng-rong,XU Zhen-yuan.A new method of studying the dynamical behaviour of the sine-Gordon equation[J].Phys Lett A,1995,204(5):343-346.
|
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[5] | LI Wen-cheng, DENG Zi-chen. Adaptive Explicit Magnus Numerical Method for Nonlinear Dynamical Systems[J]. Applied Mathematics and Mechanics, 2008, 29(9): 1009-1016. |
[6] | JIAN Yong-jun, E Xue-quan, ZHANG Jie. Damping of Vertically Excited Surface Wave in a Weakly Viscous Fluid[J]. Applied Mathematics and Mechanics, 2006, 27(3): 372-378. |
[7] | MA Jun-hai, CHEN Yu-shu, XIN Bao-gui. Study on Prediction Methods for Dynamic Systems of Nonlinear Chaotic Time Series[J]. Applied Mathematics and Mechanics, 2004, 25(6): 551-557. |
[8] | LI Zi-zhen, XU Cai-lin, WANG Wan-xiong. Two-Dimensional Nonlinear Dynamic System Model of Interspecific Interaction and Numerical Simulation Research on It[J]. Applied Mathematics and Mechanics, 2003, 24(7): 739-746. |
[9] | WU Zhi-qiang, CHEN Yu-shu. Classification of Bifurcations for Nonlinear Dynamical Problems With Constraints[J]. Applied Mathematics and Mechanics, 2002, 23(5): 477-482. |
[10] | MA Jun-hai, CHEN Yu-shu. Study on the Prediction Method of Low-Dimension Time Series That Arise From the Intrinsic Nonlinear Dynamics[J]. Applied Mathematics and Mechanics, 2001, 22(5): 441-448. |
[11] | TIAN Li-xin, LIU Yu-rong, LIU Zeng-rong. Local Attractors for the Weakly Damped Forced KdV Equation in Thin 2D Domains[J]. Applied Mathematics and Mechanics, 2000, 21(10): 1021-1027. |
[12] | Han Qiang, Zhang Shanyuan, Yang Guitong. The Study on the Chaotic Motion of a Nonlinear Dynamic System[J]. Applied Mathematics and Mechanics, 1999, 20(8): 776-782. |
[13] | Ma Junhai, Chen Yushu, Liu Zengrong. The Non-Linear Chaotic Model Reconstruction for the Exerimental Data Obtained From Different Dynamic System[J]. Applied Mathematics and Mechanics, 1999, 20(11): 1128-1134. |
[14] | Ma Junhai, Chen Yushu, Liu Zengrong. Threshold Value for Diagnosis of Chaotic Nature of the Data Obtained in Nonlinear Dynamic Analysis[J]. Applied Mathematics and Mechanics, 1998, 19(6): 480-488. |
[15] | Lin Yurui, Tian Lixin, Liu Zengrong. The Wild Solutions of the Induced Form under the Spline Wavelet Basis in Weakly Damped Forced KdV Equation[J]. Applied Mathematics and Mechanics, 1998, 19(12): 1071-1076. |
[16] | Zhang Wei, Chen Yushu. Adjoint operator Method and Normal Forms of Higher order for Nonlinear Dynamical System[J]. Applied Mathematics and Mechanics, 1997, 18(5): 421-432. |
[17] | Tian Lixin, Xu Zhenyuan. The Research of Longtime Dynamic Behavior in Weakly Damped Forced KdV Equation[J]. Applied Mathematics and Mechanics, 1997, 18(10): 953-958. |
[18] | Dai Zheng-de, zhu zhi-we. The Inertial Fractal Set for Weakly Damped Forced Koreweg-de-Vries Equation[J]. Applied Mathematics and Mechanics, 1995, 16(1): 33-40. |
[19] | Zhu Chang-jiang. Intial Value Problem for High Dimensional Dynamic Systems[J]. Applied Mathematics and Mechanics, 1995, 16(3): 263-266. |
[20] | C. S. Hsu, Xu Jian-xue. The Global Analysis of Higher Order Non-linear Dynamical Systems and the Application of Cell-to-Cell Mapping Method[J]. Applied Mathematics and Mechanics, 1985, 6(11): 953-962. |