The KdV equation under periodic boundary conditions and its perturbations

Huang Guan, Sergei Kuksin

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Abstract

In this paper we discuss properties of the Korteweg-de Vries (KdV) equation under periodic boundary conditions, especially those which are important for studying perturbations of the equation. We then review what is known about the long-time behaviour of solutions for perturbed KdV equations.

Original languageEnglish
Pages (from-to)R61-R88
JournalNonlinearity
Volume27
Issue number9
DOIs
Publication statusPublished - 1 Sept 2014
Externally publishedYes

Keywords

  • KAM
  • KdV
  • averaging
  • perturbed KdV
  • random perturbation

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Guan, H., & Kuksin, S. (2014). The KdV equation under periodic boundary conditions and its perturbations. Nonlinearity, 27(9), R61-R88. https://doi.org/10.1088/0951-7715/27/9/R61