American Institute of Mathematical Sciences

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October  1998, 4(4): 783-793. doi: 10.3934/dcds.1998.4.783

Attractor for the dissipative Hamiltonian amplitude equation governing modulated wave instabilities

Boling Guo 1, and  Zhengde Dai 2,

1. 

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088
2. 

Department of Mathematics, Yunnan University, Kunming 650091, China

Received  April 1997 Revised  May 1998 Published  July 1998

In this paper, the long time behavior of solution for the dissipative Hamiltonian amplitude equation governing modulated wave instabilities is considered. First the global weak attractor for this equation in $E_1$ is constructed. And then by exact analysis of energy equations, it is showed that the global weak attractor is actually the global strong attractor in $E_1$.
Keywords: global attractor, dissipation., Hamiltonian amplitude equation.
Mathematics Subject Classification: 35K57, 35B4.
Citation: Boling Guo, Zhengde Dai. Attractor for the dissipative Hamiltonian amplitude equation governing modulated wave instabilities. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 783-793. doi: 10.3934/dcds.1998.4.783
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