Averaging Normal Forms for Partial Differential Equations with Applications to Perturbed Wave Equations

作者: F. Verhulst

DOI: 10.1007/978-0-8176-4899-2_29

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摘要: Normalization and normal forms play an important part in mathematical analysis algebra. For instance, n×n-matrices can be put Jordan form. Such example also makes it clear that normalization is not a unique procedure as the choice of matrices depends on its purpose. In case there vast literature with many possibilities, but all special cases other problems well, general aim simplification object by transformation.

参考文章(11)
Alexander P Seyranian, Alexei A Mailybaev, Multiparameter Stability Theory with Mechanical Applications ,(2004)
Ferdinand Verhulst, Jan A. Sanders, Averaging Methods in Nonlinear Dynamical Systems ,(1985)
Ferdinand Verhulst, Perturbation Analysis of Parametric Resonance. Encyclopedia of Complexity and Systems Science. pp. 6625- 6639 ,(2009)
M. S. Krol, On the Averaging Method in Nearly Time-Periodic Advection-Diffusion Problems SIAM Journal on Applied Mathematics. ,vol. 51, pp. 1622- 1637 ,(1991) , 10.1137/0151083
F. Verhulst, J. M. Tuwankotta, Symmetry and Resonance in Hamiltonian Systems Siam Journal on Applied Mathematics. ,vol. 61, pp. 1369- 1385 ,(2001) , 10.1137/S0036139900365323
Taoufik Bakri, Hil G. E. Meijer, Ferdinand Verhulst, Emergence and bifurcations of Lyapunov manifolds in nonlinear wave equations Journal of Nonlinear Science. ,vol. 19, pp. 571- 596 ,(2009) , 10.1007/S00332-009-9045-2
Enrique Sanchez-Palencia, Methode de centrage-estimation de l'erreur et comportement des trajectoires dans l'espace des phases International Journal of Non-Linear Mechanics. ,vol. 11, pp. 251- 263 ,(1976) , 10.1016/0020-7462(76)90004-4
J. J. Heijnekamp, M. S. Krol, F. Verhulst, Averaging in non-linear advective transport problems Mathematical Methods in the Applied Sciences. ,vol. 18, pp. 437- 448 ,(1995) , 10.1002/MMA.1670180603