A determining form for the damped driven nonlinear Schrodinger equation-Fourier modes case Academic Article

abstract

• 2014 Elsevier Inc. In this paper we show that the global attractor of the 1D damped, driven, nonlinear Schrdinger equation (NLS) is embedded in the long-time dynamics of a determining form. The determining form is an ordinary differential equation in a space of trajectories X=Cb1(R,PmH2) where P m is the L 2 -projector onto the span of the first m Fourier modes. There is a one-to-one identification with the trajectories in the global attractor of the NLS and the steady states of the determining form. We also give an improved estimate for the number of the determining modes.

authors

• Titi, Edriss

published proceedings

• JOURNAL OF DIFFERENTIAL EQUATIONS

author list (cited authors)

• Jolly, M. S., Sadigov, T., & Titi, E. S.

citation count

• 13

complete list of authors

• Jolly, Michael S||Sadigov, Tural||Titi, Edriss S

publication date

• April 2015

publisher

• Elsevier  Publisher

published in

• Journal of Differential Equations  Journal

keywords

• Determining Forms
• Determining Modes
• Determining Nodes
• Inertial Manifolds
• Nonlinear Schrodinger Equation

Digital Object Identifier (DOI)

• 10.1016/j.jde.2014.12.023

start page

• 2711

end page

• 2744

volume

• 258

issue

• 8

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jde.2014.12.023