Attractor for the dissipative Hamiltonian amplitude equation governing modulated wave instabilities

Boling Guo; Zhengde Dai

doi:10.3934/dcds.1998.4.783

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1998, Volume 4, Issue 4: 783-793. Doi: 10.3934/dcds.1998.4.783

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Attractor for the dissipative Hamiltonian amplitude equation governing modulated wave instabilities

Boling Guo^1, and
Zhengde Dai²

1.
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088
2.
Department of Mathematics, Yunnan University, Kunming 650091

Received: March 31, 1997

Revised: April 30, 1998

Published: September 1998

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Abstract

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 $E_1$.

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Mathematics Subject Classification: 35K57, 35B40.

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