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Wavelet approximate inertial manifold in nonlinear solitary wave equation. (English) Zbl 0973.35169

Summary: This paper studies the dynamical behavior of a weakly damped forced Korteweg-de Vries (KdV) equation in a wavelet basis and introduces the wavelet approximate inertial manifold as well as the wavelet Galerkin solution of weakly damped forced KdV equation. The results include theorems that for the KdV equation the wavelet approximate inertial manifold (WAIM) exists and sets up the wavelet Galerkin method of the equation. Error estimates are given by using the WAIM.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
41A30 Approximation by other special function classes
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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