Averaging Normal Forms for Partial Differential Equations with Applications to Perturbed Wave Equations
Normalization and normal forms play an important part in mathematical analysis and algebra. For instance, n×n-matrices can be put in Jordan normal form. Such an example also makes it clear that normalization is not a unique procedure as the choice of normalization of matrices depends on its purpose. In the case of matrices there is a vast literature with many possibilities, but in all special cases and in other mathematical problems as well, the general aim of normalization is a simplification of the object by transformation.
KeywordsPeriodic Solution Normal Form Parametric Resonance Parametric Excitation Tidal Basin
Unable to display preview. Download preview PDF.
- [BMV]Bakri, T., Meijer, H.G.E, Verhulst, F.: Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations, J. Nonlinear Sci. (to appear).Google Scholar
- [Bu93]Buitelaar, R.P.: The Method of Averaging in Banach Spaces, Ph.D. Thesis, University of Utrecht, The Netherlands (1993).Google Scholar
- [RaEtAl99]Rand, R.H., Newman, W.I., Denardo, B.C., Newman, A.L.: Dynamics of a nonlinear parametrically-excited partial differential equation, in Proc. Design Engng. Techn. Conferences 3 (1995), 57–68. (See also Chaos, 9, 242–253 (1999).)Google Scholar
- [Sa76]Sanchez-Palencia, É.: Méthode de centrage - estimation de l'erreur et comportement des trajectoires dans l'espace des phases. Internat. J. Nonlinear Mech., 11, 251–263 (1976).Google Scholar
- [Ve09]Verhulst, F.: Perturbation Analysis of Parametric Resonance, in Encyclopedia of Complexity and System Science. Perturbation Theory, Gaeta, G., ed., Springer, Berlin (2009).Google Scholar