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Quasi-periodic solutions of nonlinear wave equations in the D-dimensional torus /

Many partial differential equations (PDEs) arising in physics, such as the nonlinear wave equation and the Schrödinger equation, can be viewed as infinite-dimensional Hamiltonian systems. In the last thirty years, several existence results of time quasi-periodic solutions have been proved adopting a...

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Bibliographic Details
Main Authors: Berti, Massimiliano (Author), Bolle, Philippe (Author)
Format: Book
Language:English
Published: Berlin : European Mathematical Society, [2020]
Series:EMS monographs in mathematics.
Subjects:
Nonlinear wave equations > Numerical solutions.
Hamiltonian systems.
Table of Contents:
  • KAM for PDEs and strategy of proof
  • Hamiltonian formulation
  • Functional setting-- Multiscale analysis
  • Nash-Moser theorem
  • Linearized operator at an approximate solution
  • Splitting of low-high normal subspaces up to O (E4)
  • Approximate right inverse in normal directions
  • Splitting between low-high normal subspaces
  • Construction of approximate right inverse
  • Proof of the Nash-Moser theorem
  • Genericity of the assumptions.