Wavelet approximate inertial manifold in nonlinear solitary wave equation

This paper studies the dynamical behavior of a weakly damped forced Kortewe g-de Vries (KdV) equation in a wavelet basis and introduces the wavelet app roximate inertial manifold and wavelet Galerkin solution of weakly damped f orced KdV equation. The results includes theorems that for the KdV equation the wavelet approximate inertial manifold (WAIM) exists and sets up the wa velet Galerkin method of the equation. Error estimates are given by using t he WAIM. (C) 2000 American Institute of Physics. [S0022-2488(00)02208-8].