Wavelet basis analysis in perturbed periodic KdV equation
type: Item
instance of: scholarly article
title: Wavelet basis analysis in perturbed periodic KdV equation
zbMATH Open document ID: 0936.35170
DOI: 10.1007/BF02459193
author: Dianchen Lu
author: Lixin Tian
author: Zengrong Liu
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2000-05-18T00:00:00Z
review text: This paper studies the perturbed periodic KdV equation given by \[ u_t+\varepsilon u_{xxxx}+u_{xxx}-\eta u_{xx}+\gamma u+uu_x=f,\quad u(x,t)= u(x+1,t), \quad u(x,0)= u_0(x)\in H^3(\Omega) \] where \(\Omega=[0,1]\), \(\eta, \gamma>0\) and \(f\in H^3(\Omega)\) is time independent. The purpose of the present paper is to study the long time behavior of perturbed periodic KdV equation by using a spline wavelet basis to construct the approximate inertial manifold. The essential part is the construction of the inertial manifold by using the spline wavelet basis. The method to study the approximate inertial manifold by using the spline wavelet basis originates from a paper by Goubet on the self-adjoint nonlinear evolutionary equation. But the question and the result in the present paper are different from that of Goubet's paper.
reviewed by: M. Nagase
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 37L25
zbMATH DE Number: 1322258
zbMATH Keywords: wavelet basis
zbMATH Keywords: approximate inertial manifold
zbMATH Keywords: perturbed periodic KdV equation
MaRDI profile type: Publication
cites work: On the construction of families of approximate inertial manifolds
cites work: Construction of Approximate Inertial Manifolds Using Wavelets
cites work: Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis
cites work: Exponentially small estimate for a generalized solitary wave solution to the perturbed K−dV equation
cites work: The research of longtime dynamic behavior in weakly damped forced KdV equation
Recommended article: Q4288490
Recommended article: Q4924331
Recommended article: Wavelet Study of Dynamical Systems Using Partial Differential Equations
Recommended article: Asymptotic Analysis of a Perturbed Periodic Solution for the KdV Equation
Recommended article: Q4249294
Recommended article: Wavelets generated by Riesz potentials of KdV solitons
Recommended article: The KdV equation under periodic boundary conditions and its perturbations
Recommended article: Q4896566
Recommended article: Wavelets associated with periodic basis functions
Recommended article: Solitary waves and periodic waves in a perturbed KdV equation
description: scientific article; zbMATH DE number 1322258