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Integrability of Nonlinear Systems and Perturbation Theory

  • V. E. Zakharov
  • E. I. Schulman
Part of the Springer Series in Nonlinear Dynamics book series (SSNONLINEAR)

Abstract

The theory of so-called integrable Hamiltonian wave systems arose as a result of the inverse scattering method discovery by Gardner, Green, Kruskal and Miura [1] for the Korteveg-de Vries equation. This discovery was initiated by the pioneering numerical experiment by Kruskal and Zabusky [2]. After a pragmatic phase, which was devoted to finding new soliton equations, the theory became rather complicated. One of its branches may be called the “qualitative theory of infinite-dimensional Hamiltonian systems”, to which the results reviewed in this paper belong. We consider only Hamiltonian systems possessing Hamiltonians with a quadratic part which may be transformed in normal variables to the form
$$H_0 = \sum\limits_{\alpha = 1}^N {\omega _k ^{\left( \alpha \right)} a_k ^{\left( \alpha \right)} a_k ^{*\left( \alpha \right)} dk} $$
(1.1.1)
.

Keywords

Nonlinear System Perturbation Theory Canonical Transformation Asymptotic State Periodic Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • V. E. Zakharov
  • E. I. Schulman

There are no affiliations available

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