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Attractors for fully discrete finite difference scheme of dissipative Zakharov equations. (English) Zbl 1289.65198
Summary: A fully discrete finite difference scheme for dissipative Zakharov equations is analyzed. On the basis of a series of time-uniform a priori estimates of the difference solutions, the stability of the difference scheme and error bounds of optimal order of the difference solutions are obtained in \(L^2\times H^1\times H^2\) over a finite time interval \((0, T]\). Finally, the existence of a global attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q40 PDEs in connection with quantum mechanics
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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