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# The Global Attractor of a Damped, Forced Hirota Equation in $H^1$

Published:2009-12-04
Printed: Jun 2010
• Boling Guo
• Zhaohui Huo
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## Abstract

The existence of the global attractor of a damped forced Hirota equation in the phase space $H^1(\mathbb R)$ is proved. The main idea is to establish the so-called asymptotic compactness property of the solution operator by energy equation approach.
 Keywords: global attractor, Fourier restriction norm, damping system, asymptotic compactness
 MSC Classifications: 35Q53 - KdV-like equations (Korteweg-de Vries) [See also 37K10] 35B40 - Asymptotic behavior of solutions 35B41 - Attractors 37L30 - Attractors and their dimensions, Lyapunov exponents